AD and BE are altitudes of triangle ABC. If AC = 10, BC = 18, and AD = 5, then find BE.

Guest May 13, 2022

#2**0 **

Consider the area of triangle ABC. It can be calculated two different ways.

\(\text{Area of }\triangle ABC = \dfrac{AD \times BC}2 = \dfrac{AC \times BE}{2}\)

So, by simplifying and substituting the values, we actually have \(5\times 18 = 10 \times BE\). That means BE = 9, not 15/2 which Guest suggested.

MaxWong May 14, 2022