Question

The perimeter of a rectangle is 52. The length of the rectangle is six less than the width. Find the length and width of the rectangle

Answer 1

Create expressions for the length and width of the rectangle.

• length (l): x - 6
• width (w): x

Perimeter: 2l + 2w

Substitute (x - 6) for l and (x) for w.

• 52 = 2(x - 6) + 2(x)

Distribute 2 inside the parentheses.

• 52 = 2x - 12 + 2x

Combine like terms.

• 52 = 4x - 12

Add 12 to both sides.

• 64 = 4x

Divide both sides by 4.

• x = 16

Substitute 16 for x into the length and width of the rectangle.

• length: (16) - 6 = 10
• width: (16) = 16