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?

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