The segment marked 20 is the geometric mean of the two pieces into which it splits the hypotenuse. You get the proportion
Solving,
To find b, use the fact that b is the geometric mean of the whole hypotenuse, 21 + a, and the part that is attached to it, a.
A little arithmetic shows that
.
Solving,
To find b, use the fact that b is the geometric mean of the whole hypotenuse, 21 + a, and the part that is attached to it, a.
A little arithmetic shows that