. . . . . .
Triangle is a 3-4-5 right triangle.
We find that and are parallel to
And all the right triangles are similar.
Can you finish the problem?
From the smallest triangles, we can see that by Pythagoras.
We can also see from the larger triangles that
Now note that the area of the largest rectangle is . If we evaluate the area of each smaller piece, we find
Substituting , (since we know ) will enable solving for , which will enable solving for , and finally solving for .
See how you go.