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 ?(1 point) Responses 12 12 18 18 26 26 13

Answer 1

To find the value of \( x \), we first need to express the perimeter of each figure.

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

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

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

4. Solving for \( x \): Rearranging the equation, we first subtract \( 4x \) from both sides: \[ 20 = 2x - 6 \] Next, add \( 6 \) to both sides: \[ 26 = 2x \] Divide both sides by \( 2 \): \[ x = 13 \]

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