Question

A rectangle has an area of 1050 square feet. Its width is eight feet less than twice the length. Find the measures of the length and width of the rectangle.

Answer 1

• length = 25 ft
• width = 42 ft

Explanation:

If L represents the length, then the width is (2L-8) and the area is ...

A = LW

1050 = L(2L-8)

525 = L(L-4) . . . . . divide by 2

Completing the square, we have ...

525 +4 = L² -4L +4 . . . . . add the square of half the L coefficient

529 = (L -2)² . . . .simplify

±23 = L -2 . . . . . . take the square root

L = 25 . . . . . . . the negative root doesn't work in this scenario

(2L-8) = 42 . . . width

The length is 25 feet; the width is 42 feet.