← 4-2 · Find a missing side, then sum sides as fractions · Perimeter by Tracing Every Side

Find a missing side, then sum sides as fractions · 10 practice problems

4.NF.B.34.MD.A.3

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 11 3/10 cm

The width of a rectangle is $1\dfrac{9}{20}$ cm, and its height is $2\dfrac{15}{20}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 1 9/20 cm. Its height is 2 15/20 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 1 9/20 cm.
Height = width + 2 15/20 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 20; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 20.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 2 15/20 = 1 9/20 + 2 15/20. Whole: 1+2 = 3. Fractions: 9/20 + 15/20 = 24/20. So height = 4 4/20 cm.

1\tfrac{9}{20}+2\tfrac{15}{20}=4\tfrac{4}{20}

Same-denominator add, then regroup if the fraction part reaches 20/20.

#7 Identify Subproblems 4.NF.B.3

width + height = 1 9/20 + 4 4/20 = 5 13/20 cm. This is half the perimeter.

1\tfrac{9}{20}+4\tfrac{4}{20}=5\tfrac{13}{20}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 5 13/20 = 11 6/20 = 11 3/10 cm.

2\times 5\tfrac{13}{20}=11\tfrac{6}{20}=11\tfrac{3}{10}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 11 3/10 cm

Review

Width is about 1.45 cm and height about 4.20 cm, so perimeter is about 2 x 5.65 = 11.30 cm, matching 11 3/10 cm. Units stay in cm.

Add all four sides separately (tool 1): 1 9/20 + 1 9/20 + 4 4/20 + 4 4/20 = 11 6/20 = 11 3/10 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 20 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 2 answer: 21 7/9 cm

The width of a rectangle is $4\dfrac{2}{9}$ cm, and its height is $2\dfrac{4}{9}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 4 2/9 cm. Its height is 2 4/9 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 4 2/9 cm.
Height = width + 2 4/9 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 9; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 9.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 2 4/9 = 4 2/9 + 2 4/9. Whole: 4+2 = 6. Fractions: 2/9 + 4/9 = 6/9. So height = 6 6/9 cm.

4\tfrac{2}{9}+2\tfrac{4}{9}=6\tfrac{6}{9}

Same-denominator add, then regroup if the fraction part reaches 9/9.

#7 Identify Subproblems 4.NF.B.3

width + height = 4 2/9 + 6 6/9 = 10 8/9 cm. This is half the perimeter.

4\tfrac{2}{9}+6\tfrac{6}{9}=10\tfrac{8}{9}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 10 8/9 = 21 7/9 = 21 7/9 cm.

2\times 10\tfrac{8}{9}=21\tfrac{7}{9}=21\tfrac{7}{9}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 21 7/9 cm

Review

Width is about 4.22 cm and height about 6.67 cm, so perimeter is about 2 x 10.89 = 21.78 cm, matching 21 7/9 cm. Units stay in cm.

Add all four sides separately (tool 1): 4 2/9 + 4 2/9 + 6 6/9 + 6 6/9 = 21 7/9 = 21 7/9 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 9 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 3 answer: 17 cm

The width of a rectangle is $2\dfrac{5}{14}$ cm, and its height is $3\dfrac{11}{14}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 2 5/14 cm. Its height is 3 11/14 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 2 5/14 cm.
Height = width + 3 11/14 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 14; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 14.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 3 11/14 = 2 5/14 + 3 11/14. Whole: 2+3 = 5. Fractions: 5/14 + 11/14 = 16/14. So height = 6 2/14 cm.

2\tfrac{5}{14}+3\tfrac{11}{14}=6\tfrac{2}{14}

Same-denominator add, then regroup if the fraction part reaches 14/14.

#7 Identify Subproblems 4.NF.B.3

width + height = 2 5/14 + 6 2/14 = 8 7/14 cm. This is half the perimeter.

2\tfrac{5}{14}+6\tfrac{2}{14}=8\tfrac{7}{14}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 8 7/14 = 17 = 17 cm.

2\times 8\tfrac{7}{14}=17=17

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 17 cm

Review

Width is about 2.36 cm and height about 6.14 cm, so perimeter is about 2 x 8.50 = 17.00 cm, matching 17 cm. Units stay in cm.

Add all four sides separately (tool 1): 2 5/14 + 2 5/14 + 6 2/14 + 6 2/14 = 17 = 17 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 14 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 4 answer: 12 3/4 cm

The width of a rectangle is $2\dfrac{3}{8}$ cm, and its height is $1\dfrac{5}{8}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 2 3/8 cm. Its height is 1 5/8 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 2 3/8 cm.
Height = width + 1 5/8 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 8; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 8.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 1 5/8 = 2 3/8 + 1 5/8. Whole: 2+1 = 3. Fractions: 3/8 + 5/8 = 8/8. So height = 4 cm.

2\tfrac{3}{8}+1\tfrac{5}{8}=4

Same-denominator add, then regroup if the fraction part reaches 8/8.

#7 Identify Subproblems 4.NF.B.3

width + height = 2 3/8 + 4 = 6 3/8 cm. This is half the perimeter.

2\tfrac{3}{8}+4=6\tfrac{3}{8}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 6 3/8 = 12 6/8 = 12 3/4 cm.

2\times 6\tfrac{3}{8}=12\tfrac{6}{8}=12\tfrac{3}{4}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 12 3/4 cm

Review

Width is about 2.38 cm and height about 4.00 cm, so perimeter is about 2 x 6.38 = 12.75 cm, matching 12 3/4 cm. Units stay in cm.

Add all four sides separately (tool 1): 2 3/8 + 2 3/8 + 4 + 4 = 12 6/8 = 12 3/4 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 8 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 5 answer: 24 3/5 cm

The width of a rectangle is $5\dfrac{3}{10}$ cm, and its height is $1\dfrac{7}{10}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 5 3/10 cm. Its height is 1 7/10 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 5 3/10 cm.
Height = width + 1 7/10 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 10; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 10.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 1 7/10 = 5 3/10 + 1 7/10. Whole: 5+1 = 6. Fractions: 3/10 + 7/10 = 10/10. So height = 7 cm.

5\tfrac{3}{10}+1\tfrac{7}{10}=7

Same-denominator add, then regroup if the fraction part reaches 10/10.

#7 Identify Subproblems 4.NF.B.3

width + height = 5 3/10 + 7 = 12 3/10 cm. This is half the perimeter.

5\tfrac{3}{10}+7=12\tfrac{3}{10}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 12 3/10 = 24 6/10 = 24 3/5 cm.

2\times 12\tfrac{3}{10}=24\tfrac{6}{10}=24\tfrac{3}{5}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 24 3/5 cm

Review

Width is about 5.30 cm and height about 7.00 cm, so perimeter is about 2 x 12.30 = 24.60 cm, matching 24 3/5 cm. Units stay in cm.

Add all four sides separately (tool 1): 5 3/10 + 5 3/10 + 7 + 7 = 24 6/10 = 24 3/5 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 10 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 6 answer: 13 5/6 cm

The width of a rectangle is $1\dfrac{7}{12}$ cm, and its height is $3\dfrac{9}{12}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 1 7/12 cm. Its height is 3 9/12 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 1 7/12 cm.
Height = width + 3 9/12 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 12; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 12.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 3 9/12 = 1 7/12 + 3 9/12. Whole: 1+3 = 4. Fractions: 7/12 + 9/12 = 16/12. So height = 5 4/12 cm.

1\tfrac{7}{12}+3\tfrac{9}{12}=5\tfrac{4}{12}

Same-denominator add, then regroup if the fraction part reaches 12/12.

#7 Identify Subproblems 4.NF.B.3

width + height = 1 7/12 + 5 4/12 = 6 11/12 cm. This is half the perimeter.

1\tfrac{7}{12}+5\tfrac{4}{12}=6\tfrac{11}{12}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 6 11/12 = 13 10/12 = 13 5/6 cm.

2\times 6\tfrac{11}{12}=13\tfrac{10}{12}=13\tfrac{5}{6}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 13 5/6 cm

Review

Width is about 1.58 cm and height about 5.33 cm, so perimeter is about 2 x 6.92 = 13.83 cm, matching 13 5/6 cm. Units stay in cm.

Add all four sides separately (tool 1): 1 7/12 + 1 7/12 + 5 4/12 + 5 4/12 = 13 10/12 = 13 5/6 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 12 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 7 answer: 21 7/11 cm

The width of a rectangle is $4\dfrac{6}{11}$ cm, and its height is $1\dfrac{8}{11}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 4 6/11 cm. Its height is 1 8/11 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 4 6/11 cm.
Height = width + 1 8/11 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 11; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 11.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 1 8/11 = 4 6/11 + 1 8/11. Whole: 4+1 = 5. Fractions: 6/11 + 8/11 = 14/11. So height = 6 3/11 cm.

4\tfrac{6}{11}+1\tfrac{8}{11}=6\tfrac{3}{11}

Same-denominator add, then regroup if the fraction part reaches 11/11.

#7 Identify Subproblems 4.NF.B.3

width + height = 4 6/11 + 6 3/11 = 10 9/11 cm. This is half the perimeter.

4\tfrac{6}{11}+6\tfrac{3}{11}=10\tfrac{9}{11}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 10 9/11 = 21 7/11 = 21 7/11 cm.

2\times 10\tfrac{9}{11}=21\tfrac{7}{11}=21\tfrac{7}{11}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 21 7/11 cm

Review

Width is about 4.55 cm and height about 6.27 cm, so perimeter is about 2 x 10.82 = 21.64 cm, matching 21 7/11 cm. Units stay in cm.

Add all four sides separately (tool 1): 4 6/11 + 4 6/11 + 6 3/11 + 6 3/11 = 21 7/11 = 21 7/11 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 11 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 8 answer: 13 5/7 cm

The width of a rectangle is $2\dfrac{4}{7}$ cm, and its height is $1\dfrac{5}{7}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 2 4/7 cm. Its height is 1 5/7 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 2 4/7 cm.
Height = width + 1 5/7 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 7; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 7.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 1 5/7 = 2 4/7 + 1 5/7. Whole: 2+1 = 3. Fractions: 4/7 + 5/7 = 9/7. So height = 4 2/7 cm.

2\tfrac{4}{7}+1\tfrac{5}{7}=4\tfrac{2}{7}

Same-denominator add, then regroup if the fraction part reaches 7/7.

#7 Identify Subproblems 4.NF.B.3

width + height = 2 4/7 + 4 2/7 = 6 6/7 cm. This is half the perimeter.

2\tfrac{4}{7}+4\tfrac{2}{7}=6\tfrac{6}{7}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 6 6/7 = 13 5/7 = 13 5/7 cm.

2\times 6\tfrac{6}{7}=13\tfrac{5}{7}=13\tfrac{5}{7}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 13 5/7 cm

Review

Width is about 2.57 cm and height about 4.29 cm, so perimeter is about 2 x 6.86 = 13.71 cm, matching 13 5/7 cm. Units stay in cm.

Add all four sides separately (tool 1): 2 4/7 + 2 4/7 + 4 2/7 + 4 2/7 = 13 5/7 = 13 5/7 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 7 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 9 answer: 18 1/3 cm

The width of a rectangle is $3\dfrac{1}{6}$ cm, and its height is $2\dfrac{5}{6}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 3 1/6 cm. Its height is 2 5/6 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 3 1/6 cm.
Height = width + 2 5/6 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 6; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 6.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 2 5/6 = 3 1/6 + 2 5/6. Whole: 3+2 = 5. Fractions: 1/6 + 5/6 = 6/6. So height = 6 cm.

3\tfrac{1}{6}+2\tfrac{5}{6}=6

Same-denominator add, then regroup if the fraction part reaches 6/6.

#7 Identify Subproblems 4.NF.B.3

width + height = 3 1/6 + 6 = 9 1/6 cm. This is half the perimeter.

3\tfrac{1}{6}+6=9\tfrac{1}{6}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 9 1/6 = 18 2/6 = 18 1/3 cm.

2\times 9\tfrac{1}{6}=18\tfrac{2}{6}=18\tfrac{1}{3}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 18 1/3 cm

Review

Width is about 3.17 cm and height about 6.00 cm, so perimeter is about 2 x 9.17 = 18.33 cm, matching 18 1/3 cm. Units stay in cm.

Add all four sides separately (tool 1): 3 1/6 + 3 1/6 + 6 + 6 = 18 2/6 = 18 1/3 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 6 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!

Variant 10 answer: 16 4/5 cm

The width of a rectangle is $3\dfrac{5}{15}$ cm, and its height is $1\dfrac{11}{15}$ cm longer than the width. Find the sum of the lengths of the four sides of this rectangle, in cm.

Show solution

Understand

A rectangle has width 3 5/15 cm. Its height is 1 11/15 cm longer than the width. I must find the perimeter (the sum of all four side lengths) in cm.

Givens

Width = 3 5/15 cm.
Height = width + 1 11/15 cm.
A rectangle has two widths and two heights.

Unknowns

The perimeter (sum of the four sides) of the rectangle.

Constraints

Fraction parts share denominator 15; perimeter = 2 x (width + height).

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

First find the height by adding to the width, then apply the rectangle perimeter formula P = 2 x (width + height). Two clean subproblems, both with denominator 15.

Execute

#7 Identify Subproblems 4.NF.B.3

Height = width + 1 11/15 = 3 5/15 + 1 11/15. Whole: 3+1 = 4. Fractions: 5/15 + 11/15 = 16/15. So height = 5 1/15 cm.

3\tfrac{5}{15}+1\tfrac{11}{15}=5\tfrac{1}{15}

Same-denominator add, then regroup if the fraction part reaches 15/15.

#7 Identify Subproblems 4.NF.B.3

width + height = 3 5/15 + 5 1/15 = 8 6/15 cm. This is half the perimeter.

3\tfrac{5}{15}+5\tfrac{1}{15}=8\tfrac{6}{15}

Adding one width and one height gives half the perimeter.

#7 Identify Subproblems 4.MD.A.3

Perimeter = 2 x (width + height) = 2 x 8 6/15 = 16 12/15 = 16 4/5 cm.

2\times 8\tfrac{6}{15}=16\tfrac{12}{15}=16\tfrac{4}{5}

A rectangle has two equal widths and two equal heights, so doubling the half-perimeter gives the whole.

Answer: 16 4/5 cm

Review

Width is about 3.33 cm and height about 5.07 cm, so perimeter is about 2 x 8.40 = 16.80 cm, matching 16 4/5 cm. Units stay in cm.

Add all four sides separately (tool 1): 3 5/15 + 3 5/15 + 5 1/15 + 5 1/15 = 16 12/15 = 16 4/5 cm, the same result.

Standards · min grade 4

4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Adding the mixed-number side lengths with denominator 15 and regrouping improper fractions.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Using perimeter = 2 x (width + height) to total the four sides.

💡 This only needs Grade 4 fraction adding plus the rectangle perimeter formula — two widths plus two heights!