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28 February, 13:50

Patricia wishes to have a rectangular-shaped garden in her backyard. she has 70 ft of fencing material with which to enclose her garden. letting x denote the width of the garden, find a function f in the variable x giving the area of the garden. what is its domain?

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  1. 28 February, 14:26
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    For this problem, let x be the width and y be the length of the rectangle. We use these variable to make an equation from the perimeter.

    Perimeter = 2*Length + 2*WIdth

    Perimeter = 2y + 2x

    70 = 2y + 2x

    The area of a rectangle is equal to the product of x and y. Since we want the equation in terms of x only, let's find y in terms of x.

    y = 35 - x

    Hence, the formula for area is:

    Area = xy

    Area = x (35 - x)

    Area = 35x - x²
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