Raji draws a square with a side length of x+5 cm. Ava draws a regular hexagon with a side length of x−1 cm. 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 solve for \( x \), we first need to find the perimeters of both figures and set them equal to each other.

1. Perimeter of the square: The formula for the perimeter of a square is given by: \[ \text{Perimeter}_{\text{square}} = 4 \times \text{side length} = 4 \times (x + 5) \] Therefore, the perimeter of Raji's square is: \[ 4(x + 5) = 4x + 20 \]

2. Perimeter of the hexagon: The formula for the perimeter of a regular hexagon is given by: \[ \text{Perimeter}_{\text{hexagon}} = 6 \times \text{side length} = 6 \times (x - 1) \] Therefore, the perimeter of Ava's hexagon is: \[ 6(x - 1) = 6x - 6 \]

3. Setting the perimeters equal: Since the two figures have the same perimeter, we can set the equations for the perimeters equal to each other: \[ 4x + 20 = 6x - 6 \]

4. Solving for \( x \): To solve for \( x \), we first isolate \( x \): \[ 20 + 6 = 6x - 4x \] Simplifying this gives: \[ 26 = 2x \] Dividing both sides by 2, we find: \[ x = 13 \]

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