We want to compare the theorem to the expressions in our figure. In our case, 20 is the length of the altitude, and 10 and x are the lengths of the partial segments of the hypotenuse.
AD/CD = CD/DB
⇔ 10/20 = 20/x
Now, we can find the value of x.
Since we now know the lengths of both partial segments of the hypotenuse divided by the altitude, we will use the Geometric Mean (Leg) Theorem to find the values of y and z.
We will start by finding the value of y, which corresponds to AC on this figure.
AC = sqrt(AD * AB)
⇔ y=sqrt(10(10+40))
Now, we can evaluate the right-hand side to find y.
Using a calculator, we can express y as about 22.4. Following the same reasoning, we can find z, which corresponds to CB.
CB = sqrt(DB * AB)
⇔ z=sqrt(40(10+40))
Finally, we can evaluate the right-hand side to find the value of z.
