Solving Linear Equations Online Practice

Question

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9 of 159 of 15 Items

Question
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

13
13

18
18

26

Answer 1

To find the value of \( x \) where the perimeters of Raji's square and Ava's hexagon are equal, we can set up the equation based on their perimeters.

1. Perimeter of the square:
   The side length of the square is \( x + 5 \) cm.
   Therefore, the perimeter of the square is:
   \[ P_{\text{square}} = 4 \times (x + 5) = 4x + 20 , \text{cm} \]

2. Perimeter of the hexagon:
   The side length of the hexagon is \( x - 1 \) cm.
   Therefore, the perimeter of the hexagon is:
   \[ P_{\text{hexagon}} = 6 \times (x - 1) = 6x - 6 , \text{cm} \]

3. Set the perimeters equal to each other:
   \[ 4x + 20 = 6x - 6 \]

4. Solve for \( x \):
   \[ 20 + 6 = 6x - 4x \ 26 = 2x \ x = \frac{26}{2} = 13 \]

So the value of \( x \) is 13.