A rectangular field having an area of 2700 square meters is enclosed by a fence. An additional fence is to be used to divide the field down the middle. The cost of the fence down the middle is $12 per meter, and the fence along the sides costs $18 per meter. The dimensions of the field such that the cost of the fencing will be the least are

A)40 m by 67.5 m
B)45 m by 60 m
C)30 m by 90 m
D)54 m by 50 m
E)27 m by 100 m

Question

A rectangular field having an area of 2700 square meters is enclosed by a fence. An additional fence is to be used to divide the field down the middle. The cost of the fence down the middle is $12 per meter, and the fence along the sides costs $18 per meter. The dimensions of the field such that the cost of the fencing will be the least are
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A)40 m by 67.5 m
B)45 m by 60 m
C)30 m by 90 m
D)54 m by 50 m
E)27 m by 100 m

Quizplus · Accepted Answer

To minimize the cost, the field should be as close to a square as possible. The dimensions 45 m by 60 m give a perimeter of 210 m, which minimizes the cost of the fencing.

A Rectangular Field Having an Area of 2700 Square Meters