Question

John wants to construct a dog pen at the back of his garage. he will use the wall of the garage as one side of the pen and will construct the rest of the rectangular pen from 28 yards of fencing. what is the maximum area that can be achivied for the dog pen? square yards

Answer 1

If . he will use the wall of the garage as one side of the pen and will construct the rest of the rectangular pen from 28 yards of fencing. The maximum area that can be achieved for the dog pen is: 392 yards².

Maximum area

Let x represent the  width of the fence

Let the two widths represent  2x

Let the  length of one side represent 28-x

Let A represent Area

Hence,

A=x(28-x)

=-x²+28x

Using calculus or vertex = -b/2a,

x value = -28/-2

x = 14

2x = 28

So,

Maximum area= 14 ×28

Maximum area = 392 yards²

Therefore the maximum area is 392 yards².

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