Answer:
width = 6
length = 9
Explanation:
Perimeter = 2(length + width) or P = 2(l + w)
2(l + w) = 50
l + w = 25
l = 25 - w
Area = length x width or A = lw
lw = 114
Substitute l = 25 - w into the lw = 114
(25 - w)w = 114
25w - w^2 = 114
-w^2 + 25w - 114 = 0
=> w^2 - 25w + 114 = 0
we have x = [-b ± √(b^2 - 4ac)] / 2a
w = [-(-25) ± √((-25)^2 - 4(1)(114)))] / 2(1)
w = [25 ± √(625 - 456)] / 2
w = [25 ± √(169)]/2
w = [25 ± 13]/2
w = [25 + 13]/2 = 38/2 = 14
or
w = [25 - 13]/2 = 12/2 = 6
if width = 14, length = 25 - 14 = 11
then area = 14 x 11 = 154, this is incorrect answer
if width = 6, length = 25 - 6 = 19
then area = 6 x 19 = 114, this is correct answer