#### Answer

$x=y=25~m$

#### Work Step by Step

$P = 2(x+y)$
$100 = 2(x+y)$
$50 = x + y$
$50 - x = y$
$A = xy$
$A(x) = x(50 - x)$
$A(x) = 50x - x^2$
Derivative:
$A'(x) = 50 - 2x$
$0 = 50 - 2x$
$2x = 50$
$x = 25$
Substitute:
$50 - 25 = y$
$25 = y$
Solve for $x$:
$50-x=25$
$x=25$