Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB=8 and AD=4, what is the length of AC?

Answer 1

AC = 16

Explanation:

In ΔABC & ΔABD

angle ABC = angle ADB ---- (each 90°)

angle BAD = angle CAB ---- (common)

so, therefore

ΔABC ~ ΔABD --- (by AA similarity)

by similarity in ΔABC & ΔABD

AB/AC = AD/AB

8/AC = 4/8

AC = 8×8÷4

AC = 16