In the diagram below BC, is an altitude of ABD. What is the length of CD ? If necessary, round your answer to two decimal places.
(picture below)

Question

anonymous · Answer

|dw:1357782485881:dw|

anonymous · Answer

so im gonna use the pythagorean theorem?

mathstudent55 · Answer

|dw:1357783479900:dw|
In a right triangle, if the altitute to the hypotenuse is drawn, then the length of the altitude is the geometric mean of the two segments of the hypotenuse.

The geometric mean of two numbers a and b is sqrt(ab)

Let x = CD
The two segments of the hypotenuse are 
AC = 5, and
CD = x
The altitude measures 12

12 is the geometric mean of 5 and x:
12 = sqrt(5x)
Solve for x

anonymous · Answer

would it be 0.41?

mathstudent55 · Answer

12 = sqrt(5x)
Square both sides:
144 = 5x
Divide both sides by 5:
x = 28.8