Patricia wishes to have a rectangularshaped garden in her ba

Patricia wishes to have a rectangular-shaped garden in her backyard. She has 74 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? In this application, Patricia wishes to have a rectangular-shaped garden in her backyard. Let x denote the width of the garden. We find a function fin the variable x giving the area of the garden, and then find the function\'s domain. We recognize that the perimeter of the garden (i.e., distance around the garden\'s four sides) must

Solution

We have given ;

x= width of the garden

y= length of the garden

Now we know that perimeter of the graden= 2(x+y)

Now we have given perimeter = 74

=> 2(x+y) = 74

=> x+y = 74/2 = 37 => y= 37-x ---------------(1)

Now Area of a rectangle = length* width

=> A= xy = x (37-x)

=> A(x) = 37x - x^2

Now Domain is the set of x values for which the area function A(x) is defined. Now we can see that the area function is defined for all x

Hence domain = All real numbers