Question

The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft2. What is the length of the field?
80 ft
100 ft
120 ft
140 ft

Answer 1

Let the length be L (ft). Then width = L − 20, and area L(L − 20) = 12,000.

Solve L^2 − 20L − 12,000 = 0.
L = [20 ± sqrt(20^2 + 4·12,000)]/2 = [20 ± sqrt(48,400)]/2 = [20 ± 220]/2.

Positive solution: L = (20 + 220)/2 = 120 ft.

Answer: 120 ft.