Another cool optimization problem

1. The problem statement, all variables and given/known data

find the dimensions of a rectangle with perimeter 100m whose area is as large as possible


2. Relevant equations

area = XY

100 = 2x + 2y

y= 100/4x

x(100/4x)

(400x - 400x)/16x^2

1/16x^2 = 0
3. The attempt at a solution

well........
am lost

 

2y = 100/2x

y = (100/2x) * .5

 

am trying to solve for y

 

y = (100/2)-x

 

find the derivates of 50x-x^2
50-2x=0
x=25
100=2(25)+2y

 

y= 25

 

thanks alot. care for one more problem?