Maximum area of rectangle with given perimeter.

**scubasteve94** · May 10th 2010, 03:31 AM

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

any help would be great!

**mr fantastic** · May 10th 2010, 03:38 AM

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.

**BobBali** · May 10th 2010, 04:47 AM

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 $y = -2x+50$

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