Answer:
x=6
Step-by-step explanation:
Hi there!
<u>1) Determine the perimeter of the square</u>
We're given that the perimeters of the square and the rectangle are equal. Therefore, after finding the perimeter of the square, we will also know the perimeter of the rectangle.
Find the side length of the square using the area formula:
where l is the side length
Plug in the given area 121 in.²
Take the square root of both sides
Therefore, the side length of the square is 11 inches. Plug this into the perimeter formula:
where l is the side length
Therefore, the perimeter of the square is 44 inches. The perimeter of the rectangle is also 44 inches.
<u>2) Determine the value of x</u>
Use the formula for the perimeter of a rectangle:
where l is the length and w is the width
Plug in 3x and x-2 as the length and width
Plug in the perimeter 44 in.
Expand the parentheses
Add 4 to both sides to isolate 8x
Divide both sides by 8 to isolate x
Therefore, the value of x is 6.
I hope this helps!