Question

A carpenter is building a rectangular room with a fixed perimeter of 140 ft. What dimensions would yeild the maximum area? what is the maximum area?

Answer 1

rectangle length L, width W

perimeter = 2L + 2W = 140

so L = (140-2W)/2

so area A =W(140-2W)/2 = 70W - W^2

to find max area, differentiate A wrt W, set to zero and solve