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
[tex]18=\sqrt{x\times 8}[/tex] [tex][\because \text{Geometric mean of }a,b,c:b=\sqrt{ac}][/tex]
[tex]18^2=8x[/tex]
[tex]324=8x[/tex]
Divide both sides by 8.
[tex]\dfrac{324}{8}=x[/tex]
[tex]40.5=x[/tex]
Therefore, the value of x is 40.5.
