Find x in triangle ABC using geometric means.​

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

Let attitude from A touches the hypotenuse at point D.

Using this in the given triangle, we get

Taking square root on both sides, we get

Side cannot be negative. Therefore, the only value of x is 6.