Question

A dilation with scale factor 2 maps triangle RST to triangle R'S'T'. The perimeter of triangle RST is 60 ,what is the perimeter of triangle R'S'T'?

Answer 1

Given:

A dilation with scale factor 2 maps triangle RST to triangle R'S'T'.

The perimeter of triangle RST is 60 units.

To find:

The perimeter of triangle R'S'T'.

Solution:

We know that the dilated figure is similar to the given figure.

The scale factor is 2. It means the side length of the dilated figure is twice then the original figure. So, the ratio of side of original figure to side of dilated figure is 1:2.

Let the  perimeter of triangle R'S'T' be x.

The ratio of perimeters of similar figure is equal to the ratio of the corresponding sides of similar figures.

$\dfrac{\text{Perimeter of }RST}{\text{Perimeter of }R'S'T'}=\dfrac{1}{2}$

$\dfrac{60}{x}=\dfrac{1}{2}$

$60\times 2=1\times x$

$120=x$

Therefore, the perimeter of triangle R'S'T' is 120.