Solve the problem
-A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the dimensions of the playground that maximize the total Enclosed area.
A)150 ft by 150 ft
B)50 ft by 225 ft
C)100 ft by 150 ft
D)75 ft by 150 ft

Question

Quizplus · Accepted Answer

To maximize the area, let the length be x and the width be y. The total fencing used is 2x + 3y = 600. Solving for y gives y = (600 - 2x)/3. The area A = x*y = x(600 - 2x)/3. To maximize A, take the derivative and set it to zero. Solving gives x = 150, y = 100, so the dimensions are 100 ft by 150 ft.

Solve the Problem -A Rectangular Playground Is to Be Fenced Off and Divided