In a triangle, the measure of an altitude drawn from the vertex of right angle to its hypotenuse

is the geometric mean between the measures of the two segments of the hypotenuse.

So, the measure of the altitude EH is the geometric mean of GH and HF.

Find GH.

               (Apply segment addition postulate)

                (Substitute )

                           (Subtract each side by 12)

Find the geometric mean of GH and HF.

Geometric mean is positive number x of two positive numbers where the proportion

a : x = x : b is true. The proportion can be written as fractions  .

Write the proportion from the definition of geometric mean.

                   (Substitute )

          (Apply cross products property)

                    (Multiply: ))

                     (Take the positive square root of each side)

                        ()

The measure of the altitude EH is 6.4.