Double the side

The idea

The ratio of perimeter to side is 4 : 1 for all squares and 3 : 1 for all equilateral triangles; it stays fixed as the shape gets larger or smaller.

Make it twice as long

A square has side a and perimeter 4a. Now double the side: the new square has side 2a.

What happens to the perimeter of the square?

• It doubles too
• It becomes four times as big
• It stays the same

Larger and smaller

Change the size with − and +. The perimeter is laid out straight below the shape. Try two sizes of each shape.

Always the same number of sides

The ratio of perimeter to side is 4 : 1 for all squares and 3 : 1 for all equilateral triangles. It stays fixed as the shape gets larger or smaller.

Double the side and the perimeter doubles too. The perimeter is always the same number of sides: 4 for a square, 3 for an equilateral triangle.

Notes

The ratio of perimeter to side is 4 : 1 for all squares and 3 : 1 for all equilateral triangles. It stays fixed as the shape gets larger or smaller.

Check yourself

A square of side 5 m has perimeter 20 m. A bigger square has side 10 m. What is its perimeter?

Answer: 40 m

The perimeter doubles too: 2 × 20 = 40 m. Check: 4 × 10 = 40.

The side of a square becomes 3 times as long. Its perimeter becomes…

An equilateral triangle has perimeter 21 cm. What is its side?

Answer: 7 cm

Perimeter ÷ 3 = 21 ÷ 3 = 7 cm.

For equilateral triangles, the ratio of perimeter to side is…

• 9 times as long. The perimeter is 4a. When a is tripled, 4a is only tripled.
• 12 times as long. The 4 in 4a stays 4. Only the side is tripled.
• 3 times as long — correct. Yes. The perimeter is always 4 sides, and each side is 3 times as long.
• 3 : 1 — correct. Yes. Three equal sides make the perimeter.
• 4 : 1. 4 : 1 is the ratio for squares.
• 2 : 1. Two sides are not enough: the perimeter has all three.