The width of rectangle A is the sum of twice a number and 8. The length of the rectangle is 3 times as great as the width. If the perimeter is 96 feet, find the length and width.

Formula for perimeter of a rectangle = 2 (L + W)

let the number be x

width = 2x + 8

length = 3 (2x + 8)

substitute respectively

96 = 2 (2x + 8 + 3 (2x + 8)) open the bracket

96 = 2 (2x + 8 + 6x + 24) collect like terms

96 = 2 (8x + 32) open the bracket

96 = 16x + 64

collect like terms

96 - 64 = 16x

32 = 16x

divide both sides by 16

32/16 = 16x/16

2 = x

therefore, the width = 2x + 8 = 2 (2) + 8 = 4 + 8 = 12.

and the length = 3 (2x + 8) = 6x + 24 = 6 (2) + 24 = 12 + 24 = 36.