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# Suppose that you have 20 linear feet of fencing

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Suppose that you have 20 linear feet of fencing, and you want to make a large rectangular garden to prevent deer from eating your vegetables.

A. Let x and y denote the side lengths of your garden. Write an equation relating x and y to the length of the fencing.

B. Write the area of the garden in terms of x and y.

C. Note that by using your equation in Part A, you can write y in terms of x. Write a formula for the area of the garden that just involves x (and not y).

D. Note that x must be in the interval [0 ft, 10 ft]. (x cannot be a negative length. If x > 10 ft, then y would be a negative length.) Use the Closed Interval Method to maximize the area in terms of x.

E. In order to maximize the area of your garden, what should the dimensions be?

Mar 15, 2021
edited by Guest  Mar 15, 2021

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A    2 x + 2y = 20

B  x*y = area in ft^2

C   y = 10 -x     then area =   x * ( 10-x)

D   Not sure what closed chord method is.....

E   5 x 5  ....a square would maximize the area if given 20 ft o' fencing

Mar 15, 2021