Question

The equilateral triangles shown below are similar 2 cm, 5 cm. What is the ratio of their perimeter?

Answer 1

We have to calculate the relation between the perimeter of similar triangles.

As the perimeter is the sum of the lengths of the sides, we can demonstrate that the relation between perimeters is equal to the scale factor between sides.

In this case, the scale factor is k=2/5.

The perimeter of the left triangle is:

`P_1=3\cdot2=6`

and the perimeter of the triangle at the right is:

`P_2=3\cdot5=15`

If we write the ratio, we get:

`(P_1)/(P_2)=(6)/(15)=(3\cdot2)/(3\cdot5)=(2)/(5)`

Answer: 2/5