Question

A regular pentagon with a perimeter of 10 cm is dilated by a scale factor of 3/2 to create a new pentagon. What is the the perimeter of the new pentagon?

Answer 1

Given:

Perimeter of a regular pentagon = 10 cm

The pentagon is dilated by a scale factor = $\dfrac{3}{2}$.

To find:

The perimeter of the new pentagon.

Solution:

If a figure is dilated by a scale factor k, then

Perimeter of new figure = k × perimeter of original figure

The scale factor is $\dfrac{3}{2}$ and the perimeter of a regular pentagon is 10 cm. So, the perimeter of a new pentagon is:

$\text{Perimeter of new pentagon}=\dfrac{3}{2}\times 10$

$\text{Perimeter of new pentagon}=3\times 5$

$\text{Perimeter of new pentagon}=15$

Therefore, the perimeter of the new pentagon is 15 cm.