perimeter of 20,000ft., what is the maximum area

Question

After an outbreak of zombie virus in remote parts of Kerplackistan, the world health organization of the world is quarantining many of the infected in mountainous area. if the quarantine zone has perimeter of 20,000ft., what is the maximum area that canbe covered by the infected?

Answer 1

For a given perimeter the figure with the greatest area is the square.

The sides of the square is 5,000 ft

The area of the. square is 25,000,000 ft²

Or

w(10,000 - w) = A

-w² + 10,000w = A

Maximum at -10000/2(-1), or 5,000.