Perimeter as decimal side sums minus overlaps

5.NBT.B.74.MD.A.3 · adapt · grade 5

Archetype: Perimeter by Tracing Every Side · step in a 11-type progression

Using a $4\ \text{m}$ length of wire without overlapping, you bent it to make one equilateral triangle like the one shown. How many meters of wire are left over?

(Figure: one equilateral triangle, with one side labeled $0.58\ \text{m}$ .)

Show solution

Understand

A 4 m piece of wire is bent (no overlap) into one equilateral triangle whose side is 0.58 m. I need to find how much wire is left over after making the triangle.

Givens

Total wire length is 4 m.
The shape made is an equilateral triangle (all three sides equal).
Each side of the triangle is 0.58 m.
No wire overlaps when bending.

Unknowns

The length of wire left over, in meters.

Constraints

An equilateral triangle has exactly 3 equal sides.
Wire used equals the triangle's perimeter; leftover = total - perimeter.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram#8 Analyze the Units

Break the task into two small steps: first the perimeter (a side-length sum for an equilateral triangle), then a subtraction from the total wire. The figure shows one labeled side, and all sides are equal, so the perimeter is 3 copies of 0.58 m. Keeping the meters consistent guards against place-value slips with decimals.

Execute

#7 Identify Subproblems 5.NBT.B.7

An equilateral triangle has three equal sides of 0.58 m, so the wire used is the sum of the three sides.

0.58 + 0.58 + 0.58 = 0.58 \times 3 = 1.74 \text{ m}

Adding three equal decimals is the same as multiplying by 3; lining up the hundredths keeps the place values straight.

#7 Identify Subproblems 5.NBT.B.7

The leftover wire is the total length minus the wire used for the triangle.

4 - 1.74 = 2.26 \text{ m}

Think of 4 as 4.00; subtracting 1.74 from 4.00 gives 2.26 by regrouping, just like subtracting whole-number money amounts.

Answer: 2.26 m

Review

The triangle uses 1.74 m, which is less than half of the 4 m wire, so a leftover of 2.26 m (a bit more than half) is sensible. Check: 1.74 + 2.26 = 4.00 m, exactly the original wire.

Use Draw a Diagram (tool 1): sketch the wire as a 4 m number line, mark off three 0.58 m hops for the triangle's sides, and read the remaining length from 1.74 m to 4 m.

Standards · min grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying 0.58 by 3 for the perimeter and subtracting that from 4.
4.MD.A.3 Apply area and perimeter formulas for rectangles in real-world problems — Treating the wire used as the triangle's perimeter (sum of side lengths).

💡 Add up the three equal sides, then subtract from the total: leftover wire is just a tidy decimal subtraction you already know!