Let's analyze the given right triangle and recall the corollary that says that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
Let's compare the theorem's corollary to the expressions in our figure. In our case, x is the altitude of the triangle, 12 and 6 are the lengths of partial segments of the hypotenuse.
AD/DC=DC/DB
⇔
12/x=x/6
Now we can use the Cross Product Property to find the value of x.
We know the length of the hypotenuse, the value for the length of a segment of the hypotenuse, and the value for the length of the leg adjacent to this segment. Therefore, we can use a corollary of the Right Triangle Altitude Theorem to write a proportion.
Let's compare the theorem's corollary to the expressions in our figure. In our case, 12+6 is the length of the hypotenuse, 12 is the length of a partial segment of the hypotenuse, and y is the length of the leg that is adjacent to the partial segment.
AB/CB=CB/DB
⇔
12+6/y=y/12
Now we can use the Cross Product Property to find the value of x.
