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?

Question

Brendan Brewer

Mathematics

7 January, 07:44

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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Daniels · Answer 1

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