Given:
A figure of a right triangle and an altitude form the right angle vertex to hypotenuse.
To find:
The value of x.
Solution:
From the given figure, it is clear that the altitude divides the hypotenuse in two segments x and 8.
Length of altitude = 18
If an altitude divide the hypotenuse in 2 segments, then according to the geometric mean theorem, the length of the altitude is the geometric mean of two segments of hypotenuse.
By using geometric mean theorem, we get
![[\because \text{Geometric mean of }a,b,c:b=√(ac)]](https://img.qammunity.org/2022/formulas/mathematics/high-school/2p0blj1r30goezt3y25mdznd4uunz51oix.png)


Divide both sides by 8.


Therefore, the value of x is 40.5.