Question

Suppose you have 52 feet of fencing to enclose a rectangular dog pen. where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

Answer 1

Maximum Area = 169 feet^2

Answer 2

Width which gives maximum area = 13 feet

Maximum Area = 169
`feet^2`

Explanation:

Given: 52 feet of fencing means Perimeter of rectangular dog pen.

If Total length of the boundary of rectangle (.i.e., Perimeter) is fixed then the rectangle with equal sides has the maximum area.

Width = x (given)

∴ for maximum area let length = x

Perimeter of rectangle = 52 feet

2 × (Length + Width) = 52

2 × ( x + x ) = 52

2 × ( 2x ) = 52

4x = 52

x =
`(52)/(4)`

x = 13 feet.

Maximum Area = Length × Width

= 13 × 13

= 169
`feet^2`

Width which gives maximum area = 13 feet

Maximum Area = 169
`feet^2`