Problema Solution
A family wants to fence in a rectangular area for a garden. One side of the garden will border their house and will not be fenced. Find the dimensions of the garden with the greatest area that can be enclosed with 56ft of fencing.
Answer provided by our tutors
let
w = the width of the rectangular area
l = the length of the rectangular area
A = l*w the area of the garden
l + 2w = 56
l = 56 - 2w
plug l = 56 - 2w into A = l*w
A = (56 - 2w)*w
A = - 2w^2 + 56w
we need to find the vertex (h, k) of the parabolic function: A = - 2w^2 + 56w
h = -b/(2a), where a = -2, b = 56
h = -56/(2*(-2))
h = 14
the function has max for w = 14 ft thus we found the width.
l = 56 - 2*14
l = 56 - 28
l = 28 ft
the width is 14 ft while the length is 28 ft.