Question

Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function a=26x-x^2, 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

perimeter = 52ft

Area= 26x-x²

Maximum width?

Maximum Area?

Max x= -b/(2a) and a is coefficient.

Max x= -26/(2*-1)= 13 ft is maximum width.

Max a = 26(13)-(13)²= 169ft²