Question 1125332: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.
Area: 16 square feet Answer by ikleyn(52775) (Show Source):
They want you find the minimum x+y under condition xy = 16.
Then y = ; x + y = .
The function f(x) = has the derivative f'(x) = - = .
The derivative is zero when x^2 - 16 = 0, or x^2 = 16,
which implies x= = 4.
Then y = = 4.
Answer. The square (4 feet x 4 feet) gives the minimal perimeter, which is 16 feet.
