The length and width of a rectangular playlot have a sum of 82 yards. What dimensions would give the maximum area?
A) Length 31 yards and width 51 yards
B) Length 40 yards and width 42 yards
C) Length 41 yards and width 41 yards
D) Length 32 yards and width 50 yards

Question

Quizplus · Accepted Answer

The maximum area for a rectangle given a fixed perimeter is achieved when the rectangle is a square. Since the sum of the length and width is 82 yards, dividing this equally gives dimensions of 41 yards by 41 yards, maximizing the area.

The Length and Width of a Rectangular Playlot Have a Sum