Question

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

Answer 1

Method 1:
The altitude in a right triangle drawn from the vertex of the right angle to the hypotenuse is the geometric mean between the 2 segment of the hypotenuse:
32 = √([44)(CD] → 32² = 44.CD & CD = 32²/44 = 23.27

Method 2
Triangles BCD & ACB are similar, then we can write:

BC/AC = CD/CB
32/44 = CD/32 → 32²/44 = CD & CD = 23.27