Question

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.

Answer 1

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.