Solve the problem
-You have 64 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.
A)length: 32 feet, width: 32 feet
B)length: 32 feet, width: 16 feet
C)length: 16 feet, width: 16 feet
D)length: 48 feet, width: 16 feet

Question

Quizplus · Accepted Answer

The maximum area of a rectangle given a fixed perimeter is achieved when the rectangle is a square. However, since one side (the side along the river) does not require fencing, the problem effectively involves only three sides. To maximize the area, the two widths and one length should be equal, making the two widths (sides perpendicular to the river) and the length (parallel to the river) use the fencing efficiently. With 64 feet of fencing and not fencing one side along the river, the best allocation is for the two widths to total 32 feet (16 feet each) and the length parallel to the river to be 32 feet, making the correct answer length: 32 feet, width: 16 feet.

Solve the Problem -You Have 64 Feet of Fencing to Enclose a Rectangular