Raji draws a square with a side length of x+5

Question

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
?(1 point)
Responses

18
18

12
12

13
13

26

Answer 1

To find the value of \( x \) given that Raji's square and Ava's hexagon have the same perimeter, we first calculate the perimeters of both shapes.

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

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

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

4. Solving for \( x \): Now, we can solve this equation for \( x \).

   \[ 4x + 20 = 6x - 6 \] Subtract \( 4x \) from both sides: \[ 20 = 2x - 6 \] Add 6 to both sides: \[ 26 = 2x \] Divide both sides by 2: \[ x = 13 \]

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