Patricia wishes to have a rectangular-shaped garden in her backyard. She has 74

Question

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

Explanation / Answer

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

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