Bryan has 180 feet of fencing to fence off his rectangular garden. he will use the wall of his house as one side of the garden. write an equation to find the area of the garden. what dimensions create the garden with the greatest area? what is the greatest area?

,length=90, width=45,Max Area=4050

Step-by-step explanation:

Let the length of the garden be x and the width be y. As Bryan is using the wall of his house as one if the length, the whole of the 180 feet if fencing will be used for covering only 3 sides of garden. Hence

180=x+2y

Area of the Garden is given as

Length × width

A=xy

Replacing value of y in above equation.

Hence it is our equation for the area of the Garden.

Differentiating wrt x

Putting

180-2x=0

x=90

Hence

y=45

Hence for x=90, y =45 we have the maximum area.

Maximum Area=90*45

A=4050