A carpenter is building a rectangular room with a fixed perimeter of 68m. What dimensions would yield the maximum area?

Question

Please solve using completing the square. I appreciate any help!

Answer 1

68/4 = 17 m

largest area for a rectangle with fixed perimeter is a square

If P = 68, the square is 17m by 17m

P = 2W + 2L, L=A/W

68 = 2W +2A/W

2A/W = 68-2W

A/W = 34 -W

A = 34W -W^2 take the derivative, set it =0 and solve for W

A'(W) = 34 -2W =0

2W =34

W= 34/2 = 17 m

2L = 68-2W = 68-34 = 34

L = 34/2 = 17 m

17m by 17m gives the maximum area = 289 square meters