We want to compare the theorem to the expressions in our figure. In our case, y is the length of the altitude, and 4 and 6 are the lengths of the partial segments of the hypotenuse.
CD = sqrt(AD * DB)
⇔ y=sqrt(4 * 6)
Now, we can find the value of y.
Using a calculator, we can express y as about 4.9.
Finding x and z
Let's go back to the given figure.
Since we know the lengths of both segments of the hypotenuse divided by the altitude, we will use the Geometric Mean (Leg) Theorem to find the values of x and z.
We will start by finding the value of x, which corresponds to AC on this figure.
AC = sqrt(AD * AB)
⇔ x=sqrt(4(4+6))
Now we can evaluate the right-hand side to find x.
Using a calculator, we can express x as about 6.3. Following the same reasoning, we can find z, which corresponds to CB.
CB = sqrt(DB * AB)
⇔ z=sqrt(6(4+6))
Finally, we can evaluate the right-hand side to find the value of z.
