Given:
The figure of a right angle triangle.
To find:
The value of x using geometric mean.
Solution:
According to the geometric mean altitude theorem, if an altitude h divides the hypotenuse in two parts a and b, then
[tex]\dfrac{a}{h}=\dfrac{h}{b}[/tex]
Let attitude from A touches the hypotenuse at point D.
Using this in the given triangle, we get
[tex]\dfrac{BD}{AD}=\dfrac{AD}{CD}[/tex]
[tex]\dfrac{12}{x}=\dfrac{x}{3}[/tex]
[tex]12\times 3=x^2[/tex]
[tex]36=x^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{36}=x[/tex]
[tex]\pm 6=x[/tex]
Side cannot be negative. Therefore, the only value of x is 6.
