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Geometry Triangle - Equating Areas | Wizako - GRE Prep Blog

Geometry Triangle – Equating Areas

October 8, 2012 By K S Baskar Leave a Comment

In a triangle ABC, AB = 16, AC = 9. Find the length of the altitude to BC if the circumradius is 9.

Answer: 8
Explanation:

Consider the figure below.

We know that,
Area of a triangle = abc/4R where a,b,c are the sides of the triangle and R is the circumradius.
Hence,

(AB x BC x AC)/4R = (1/2) x BC x AD

(16 x BC x 9)/36 = (1/2) x BC x AD

Therefore, AD = 8.

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