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

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

Answer: 162 in²

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.