Problema Solution
Maria has 24 feet of fence.she wants to make the biggest rectangular area possible for her dog to play in. What length should she make each side of the dig pen?
Answer provided by our tutors
let
w = the width of the rectangular area
l = the length of the rectangular area
the perimeter is 24 ft that is:
2(l + w) = 24 divide both sides by 2
l + w = 12
l = 12 - w
the area A = length*width:
A = l*w
plug l = 12 - w into the last equation:
A = (12 - w)w
A = -w^2 + 12w
we need to find the vertex of the parabolic function A = -w^2 + 12w
since the quotient in front of w^2 is -1 < 0 the function has maximum in w = -b/(2a) where a = -1 and b = 12
w = -12/(2*(-1))
w = 6 ft
l = 12 - 6
l = 6 ft
she should make each side to be 6 ft, that is, instead of rectangular, she should make a square area with length of the side equal to 6 feet.