Question

Given right triangle ABC with altitude B D drawn to hypotenuse AC. If

AD = 15 and DC = 12, what is the length of BD in simplest radical
form?

Answer 1

3√20

Explanation:

ΔABC & ΔADB & ΔBDC are similar triangles as their respecting vertices are the same values.

Therefore:

AD : BD = BD : CD (see ΔADB & ΔBDC)

15 : BD = BD : 12

BD² = 15 × 12

BD = √180

= 3√20