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

 May 13, 2022
 #1
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BE = 15/2.

 May 13, 2022
 #2
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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.

 May 14, 2022

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