Find the dimensions that produce the maximum floor area for a one-story house that is rectangular in shape and has a perimeter of 162 ft. Round to the nearest hundredth, if necessary.

Answer 1

Let x and y be the dimensions of the floor.

Perimeter, p = 2x+2y = 162

2y = 162-2x

y = 81-x

Area, A = xy = 81x-x²

Take the derivative of A with respect to x, set to zero and solve for x.

A' = 81-2x

x = 81/2 = 40.5 feet

y = 81=81/2= 81/2 = 40.5 feet