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)

Question

Responses

13
13

26
26

12
12

18

Answer 1

To solve for \( x \), we first need to find the perimeters of both the square and the hexagon.

1. The perimeter of a square is given by the formula: \[ \text{Perimeter of square} = 4 \times \text{side length} = 4(x + 5) \]

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

Since the two figures have the same perimeter, we can set the two perimeter expressions equal to each other: \[ 4(x + 5) = 6(x - 1) \]

Now, we'll solve this equation for \( x \):

1. Distribute on both sides: \[ 4x + 20 = 6x - 6 \]

2. Rearrange the equation to find \( x \): \[ 20 + 6 = 6x - 4x \] \[ 26 = 2x \]

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

Therefore, the value of \( x \) is \( 13 \). The equation to solve was \( 4(x + 5) = 6(x - 1) \).

The answer is: \[ \boxed{13} \]