Given:
A figure of a right triangle.
To find:
The value of x.
Solution:
According to the geometric mean attitude theorem, if an altitude is drawn from the right angle vertex to the hypotenuse, then the altitude is the geometric mean of segments of hypotenuse.
Using geometric mean attitude theorem, we get
[tex]\dfrac{3}{x}=\dfrac{x}{5}[/tex]
[tex]3\times 5=x\times x[/tex]
[tex]15=x^2[/tex]
[tex]\pm \sqrt{15}=x[/tex]
But side cannot be negative. So,
[tex]\sqrt{15}=x[/tex]
Therefore, the value of x is [tex]\sqrt{15}[/tex].
