Lets call the height if the rectangle h and the width of the rectangle x.Code:c |\ | \ | \ | \ 120|____\ | x |\ | | \ | h| \ |____|___\ b 50 ^ a | | (50-x)

Using similar triangles, the height and width can be expressed as:

120 / 50 = h / (50-x)

Therefore

Now the area of a reactangle is width times height.

The width is x. The height is

Therefore, the area of the rectangle is

The maximum area is found by finding the maximum turning point.

I'll leave that part for you.