The width of a rectangle is twice it’s height if the perimeter is 54 inches find the area

The area is 162. 

You can get this by solving for the sides. One side will be 9 and the other will be 18. This is because the perimeter must be 6x since one side is x and the other would be 2x. 

Let the height be x.
⇒ Height = x

The width of a rectangle is twice it’s height.
⇒ Width = 2x

Perimeter = 54
⇒2 (x + 2x) = 54

Solve x:
2 (x + 2x) = 54

Combine like terms:
2 (3x) = 54

Distribute 2:
6x = 54

Divide both sides by 6:
x = 9

Height = x = 9
Width = 2x = 2(9) = 18

Area = 9 x 18 = 162 in²

162 in²

Here, feel free to ask if there are any questions