There is a rectangle inside an isosceles triangle. One side of the rectangle is on the base of the isosceles triangle. The 2 corners on the other side of the rectangle are touching the equal lengths of the isosceles triangle.

Image:

Attachment 19524 *"Write down, in terms of x the height, h, of the rectangle."*
Here's what I came up with:

The longer length of the triangle is

The hypotenuse of the smaller bottom left/right right angle triangle + the hypotenuse of the smaller top left/right right angle triangle = sqrt(106.25)

The equation becomes:

That doesn't seem correct and seems way too complex. I cannot simplify it down to just h=...

Can anyone help me?