Question

What are the values the values of a and b?

Answer 1

The segment marked 20 is the geometric mean of the two pieces into which it splits the hypotenuse. You get the proportion


`(20)/(a) = (21)/(20)`

Solving,


`21a =(20)(20) \\ 21a = 400 \\ a = (400)/(21)`

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.


`(b)/(a) = (21+a)/(b)`

A little arithmetic shows that
`21+a = (841)/(21)`.


`(b)/((400)/(21)) = ((841)/(21))/(b) \\ b^2 = (336400)/(441) \\ b=(580)/(21)`