word problem.

Question

Among all rectangles that have a perimeter of 134, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Answer 1

Area = length x width
A = Lw

Perimeter= 2 x length + 2 x width
P = 2L + 2w

134 = 2L + 2w

67 = L+w ---> L= 67-w


Area function in terms of width :

A(w) = (67 - w)w

The vertex of this parabola occurs at w=33.5

The max area is (67 - 33.5)*33.5 = 1122.25