Question

Suppose a regular pentagon with a perimeter of 34 inches was dilated by a scale factor of 0.25. Fill in the blanks in the following sentences. Do not round your answers.
The pentagon’s side length before the dilation was in.
The new side length after the dilation was in., and its perimeter after the dilation was in.

Answer 1

Answer:

$6.8\ \text{in}$

$8.5\ \text{in}$

$1.7\ \text{in}$

Step-by-step explanation:

Perimeter of the pendulum = 34 inches

Scale factor = 0.25

x = Length of side of pentagon

$5x=34\\\Rightarrow x=\dfrac{34}{5}\\\Rightarrow x=6.8\ \text{in}$

The pentagon’s side length before the dilation was $6.8\ \text{in}$.

New perimeter of the pentagon

$34\times 0.25=8.5\ \text{in}$

New perimeter of the pentagon is $8.5\ \text{in}$.

$5x=8.5\\\Rightarrow x=\dfrac{8.5}{5}\\\Rightarrow x=1.7\ \text{in}$

The new side length of the perimeter is $1.7\ \text{in}$.