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zhuklara [117]
3 years ago
10

Joey wants to build a rectangular garden. He plans to use a side of a river for one side of the garden, he will not place fencin

g along this side of the garden. He has 92 yards of fencing material.
What is the maximum area that will be enclosed?
Mathematics
1 answer:
NikAS [45]3 years ago
5 0

We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to 

                                                   2x + y = 92

The value of y in terms of x is equal to,

                                            y = 92 – 2x

The area is the product of the two sides,

                                                                        A = xy

Substituting,

                                                            A = x (92 – 2x) = 92x – 2x2

Solving for the derivative and equating to zero,

                                                            0 = 92 – 4x  ; x = 23

Therefore, the area of the garden is,

<span>                                                            A = 23(92 – 2(23)) = 1058 yard<span>2</span></span>

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