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 fencing along this side of the garden. he has 92 yards of fencing material. what is the maximum area that will be enclosed

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 92.

                                                       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,

                                                            A = 23(92 – 2(23)) = 1058 yard2

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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