Geometry & Figures

Problem

Use equilateral 60-degree angles and equal sides

An isosceles triangle has two equal sides of 21 cm and a base of 15 cm. I need to build an equilateral triangle whose total side length (perimeter) is the same, and find how long each of its equal sides must be.
21 cm 15 cm
GeometryMeasurement & data
Your answer
cm
How to solve
Strategy Identify Subproblems — Split the task into two small steps: first find the isosceles triangle's perimeter by adding its three sides, then share that total equally among the equilateral triangle's three sides. Checking centimeters throughout keeps the setup correct.
1STEP 1

Find the perimeter of the isosceles triangle

Both equal sides are 21 cm, so add all three sides to get the perimeter.

21 + 21 + 15 = 57 cm
2STEP 2

Share the perimeter equally among three sides

The equilateral triangle must have the same 57 cm perimeter, and all three of its sides are equal, so divide the perimeter by 3.

57 ÷ 3 = 19 cm
3STEP 3

State each side length with units

Each side of the equilateral triangle is 19 cm — the unit stays centimeters throughout.

each side = 19 cm
Answer
19 cm
57 ÷ 3 = 19 cm
Check: 19 + 19 + 19 = 57 cm, which matches the isosceles perimeter of 21 + 21 + 15 = 57 cm. Each equilateral side (19 cm) lands neatly between the isosceles base (15 cm) and equal side (21 cm), which makes sense.
Takeaway

This only needs Grade 4 perimeter-adding and equal-sharing you already know!

  • Find the perimeter of the isosceles triangle
  • Share the perimeter equally among three sides
  • State each side length with units
Where next?
Another one like thissuggested

▶ Practice — 10 problems