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

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