# Thread: Maximum area of rectangle with given perimeter.

1. ## Maximum area of rectangle with given perimeter.

Find the maximum area of a rectangular piece of ground that can be enclosed by 100 m of fencing

any help would be great!

2. Originally Posted by scubasteve94
Find the maximum area of a rectangular piece of ground that can be enclosed by 100 m of fencing

any help would be great!
A = xy.

100 = 2x + 2y => y = 50 - x.

Therefore A = x(50 - x). This is a parabola. Find the A-coordinate of its maximum turning point.

3. Area = $-X^2 + 50x$

Solve for vertex using line of symmetry equation $x = - b/2a$

$x = -50/-2 , x = 25$
Hence, find y by substituting back into $y = -2x+50$