Question

The equation A = x(x-4) describes the area, A, of a rectangular flower garden, where x is the width in feet.

What would be the width in feet of the flower garden if the area is 12 square feet?
A.2

B.6

C.4

D.7

Answer 1

The flower garden width would be 6 ft

Explanation:

A = 12 ft^2 = x(x + 4) becomes:

x^2 + 4x - 12 = 0, or (by completing the square) x^2 + 4x + 4 - 4 - 12 = 0

Thus, we have (x + 2)^2 - 16 = 0, or (x + 2)^2 = 16

Taking the square root of both sides yields x + 2 = ±4.

In this context only a positive x value makes sense: x = 2 + 4 => x = 6.

The flower garden width would be 6 ft. The other dimension would be 6 - 4, or 2, ft.