Question

BD is the altitude of right triangle ABC. If AD=3 and DC=12, what is the length of BD?

Answer 1

notice the picture below

bearing in mind that BD is making 3 similar triangles
use the proportions of the "small" and "medium" triangles

Answer 2

If BD is the altitude of right triangle ABC. If AD=3 and DC=12. The length of BD is 3 units.

What is the length?

Let denote the length of BD as x.

According to the Pythagorean Theorem:

AC²=AB²+BC²

AC is the hypotenuse AB is AD, and BC is DC.

AC²=AD²+DC²

Substitute:

AC²=3²+12²

AC²=9+144

AC²=153

Length of BD:

AC²=BD²+CD²

153=x²+12²

153=x²+144

Subtract 144 from both sides:

9=x²

Take the square root of both sides:

x=3

Therefore the length of BD is 3 units.