Question

1. the length of each side of a regular pentagon is increased by 8 inches, so the perimeter is now 65 inches. what is the original length of each side of the regular pentagon?

Explanation:

Step1: Define variables

Let \( x \) be the original length of each side of the regular pentagon. A regular pentagon has 5 sides, so the new length of each side is \( x + 8 \), and the new perimeter is \( 5(x + 8) \).

Step2: Set up equation

We know the new perimeter is 65 inches, so we set up the equation: \( 5(x + 8)=65 \).

Step3: Solve for x

First, divide both sides of the equation by 5: \( x + 8=\frac{65}{5}=13 \). Then, subtract 8 from both sides: \( x = 13 - 8 = 5 \).

Answer:

The original length of each side is 5 inches.