A question in finding maximal area

[transgalactic]

http://img233.imageshack.us/my.php?image=81951652br0.png

i showed in the link my problem

i need to find the x and y values for which we have the largest area of the
rectangle (which is trapped in the triangle)

i don't know how to build a strandart function for the area

for which
to make a derivative and find the extreme points
and then find the maximal area of this rectangle.

how do i find the area function of the rectangle

 

[HallsofIvy]

Use "similar triangles". The small right triangle above "x" is similar to the original right triangle. The ratio of x to the hypotnuse of the original triangle is equal to the ratio of h- y to h, where h is the height of the original triangle.

 

[transgalactic]

thanks