quadratic equations

Question

a recotangular field has a perimeter of 500m and an area of 14400m^2. Find the lengths of the sides.

Answer 1

A = lw

14,400 = lw

14,400/w = l

P = 2l + 2w

500 = 2(14,400/w) = 2w

Multiply both sides by w.

2w^2 - 500w + 28,800 = 0

Divide both sides by 2.

w^2 - 250w + 14,400 = 0

(w - 160)(w - 90) = 0

w - 160 = 0 or w - 90 = 0

w = 160 or w = 90 m

l = 14,400/w = 14,400/90

l = 160 m