Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular VIP section. What is the maximum area that they can fence off?

Question

it is an area question that i don't know how to solve.

Answer 1

For a rectangle of given perimeter, here 320 feet, the rectangle with the greatest are is the square.

This square shall be 80 x 80.

 

The long way

 

w represents the width

160 - w represents the length

 

A = w(160 - w)

A = 160w - w²

A = -w² + 160w

A = -(w² - 160w + 80²) + 80²     completion of square

A = -(w - 80)² + 6400  

 

Maximum at (80, 6400).