Question

Help! Need this done quickly! picture is upside down so please flip your screen! sorry! ​

Answer 1

x=6

Explanation:

Hi there!

1) Determine the perimeter of the square

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:

`A=l^2` where l is the side length

Plug in the given area 121 in.²

`121=l^2`

Take the square root of both sides

`√(121) = √(l^2) \\11=l`

Therefore, the side length of the square is 11 inches. Plug this into the perimeter formula:

`P=4l` where l is the side length

`P=4(11)\\P=44`

Therefore, the perimeter of the square is 44 inches. The perimeter of the rectangle is also 44 inches.

2) Determine the value of x

Use the formula for the perimeter of a rectangle:

`P=2(l+w)` where l is the length and w is the width

Plug in 3x and x-2 as the length and width

`P=2(3x+(x-2))\\P=2(3x+x-2)\\P=2(4x-2)`

Plug in the perimeter 44 in.

`44=2(4x-2)`

Expand the parentheses

`44=8x-4`

Add 4 to both sides to isolate 8x

`44+4=8x-4+4\\48=8x`

Divide both sides by 8 to isolate x

`(48)/(8)=(8x)/(8) \\6=x`

Therefore, the value of x is 6.

I hope this helps!