Question

A landscaper is designing a rectangular brick patio. she has enough bricks to cover 108 square feet. she wants the length of the patio to be 12 feet greater than the width. what dimensions should she use for the patio?

Answer 1

First, make an equation system based on the problem
An equation for "she has enough bricks to cover 108 square feet" is
∴ l × w = 108
An equation for "she wants the length of the patio to be 12 feet greater than the width" is
∴ l = w + 12

Second, solve the equation system by subtitution
l × w = 108
(w + 12)w = 108
w² + 12w = 108
w² + 12w - 108 = 0
(w + 18)(w - 6) = 0
w = -18 or w = 6
Because a width shouldn't be negative, -18 isn't required. The width of the patio is 6 feet.

Subtitute w with 6
l = w + 12
l = 6 + 12
l = 18
The length of the patio is 18 feet.

The dimension is 18 × 6