Polynomial Function

Question

The length of a rectangular field is twice as long as its width. If 3 feet are taken from the width, and 4 feet taken from the length, the resultant area of the field is 180 ft². Illustrate the problem, determine the polynomial function, and find the area of the original field.

Answer 1

L = 2W

(W-3)(L-4) = 180

(W-3)(2W-4) = 180

2W^2 -10W + 12 = 180

W^2 -5W + 6 = 90

W^2 -5W -84 = 0

(W-12)(W+7) = 0

W = 12

L =24

original area = LW = 24(12) = 288 ft^2