Problema Solution
a gardener is fencing off a rectangular area with a fixed perimeter of 40 ft.What is the maximum area?
Answer provided by our tutors
let
l = the length of the rectangular area
w = the width of the rectangular area
the perimeter is 40 ft
2(l + w) = 40 divide both sides by 2
l + w = 20
l = 20 - w
the area is calculated by the formula A = l*w
plus l = 20 - w into A = l*w
A = (20 - w)*w
A = -w^2 + 20w
we need to find the maximum of tha parabolic function A = -w^2 + 20w
A max = c - b^2/(4a), where a = -1, b = 20, c = 0
A max = 0 - 20^2/(4(-1))
A max = 400/4
A max = 100 ft^2
the maximum area is 100 ft^2.