From the given right triangle CD is the altitude.

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 CD is the geometric mean of BD and DA.

Find the geometric mean of BD and DA.

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 product property)

                               (Multiply: )

                             (Take the positive square root of each side)

                                ()

Find AB.

                (Apply segment addition postulate)

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

then the measure of a leg of the triangle is the geometric mean between the measures of the

hypotenuse and the segment of the hypotenuse adjacent to that leg.

Write the proportion for the leg AC.

                           (Substitute )

                     (Apply cross product property)

                                (Multiply: )

                              (Take the positive square root of each side)

                                ()

The value of x is 4.9 and y is 5.7.