Raji Draw the square with the side length of X + 5 centimeters. Ava draws a regular hexagon with a side length of X - 1 centimeter. The two figures have the same perimeter. Write an equation that allows you to solve for X. What is the value of X?

Answer 1

To find the value of \( X \), let's first express the perimeters of both the square and the regular hexagon in terms of \( X \).

1. Perimeter of the square: The formula for the perimeter \( P \) of a square with side length \( s \) is: \[ P = 4s \] For the square with side length \( X + 5 \): \[ P_{\text{square}} = 4(X + 5) = 4X + 20 \]

2. Perimeter of the hexagon: The formula for the perimeter \( P \) of a regular hexagon with side length \( s \) is: \[ P = 6s \] For the hexagon with side length \( X - 1 \): \[ P_{\text{hexagon}} = 6(X - 1) = 6X - 6 \]

Since the two figures have the same perimeter, we can set the equations equal to each other: \[ 4X + 20 = 6X - 6 \]

Now, let's solve for \( X \):

1. Rearrange the equation: \[ 20 + 6 = 6X - 4X \] \[ 26 = 2X \]

2. Divide both sides by 2: \[ X = 13 \]

Thus, the value of \( X \) is \( \boxed{13} \).