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# geometry

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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