Question

In the diagram below of right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 3 and DB = 12, what is the length of altitude CD?

Answer 1

CD = 6

Explanation:

In right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 3 and DB = 12, you want to know the length of altitude CD.

Similar triangles

The triangles ABC, ACD, and CBD are similar. In these similar triangles the ratios of long side to short side are the same for all:

CD/AD = DB/CD

CD² = AD·DB

CD = √(3·12) =√36

CD = 6

The length of altitude CD is 6.

<95151404393>