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Question

ABC is an equilateral triangle of side 2a. Find each of its altitudes.


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Solution

Finding the altitude of the equilateral triangle:

Given:

ABC is an equilateral triangle of each 2a units

Construction: DrawADBC

In right ADB

(AB)2=(AD)2+(BD)2(2a)2=(AD)2+(a)24a2=(AD)2+a24a2a2=(AD)23a2=(AD)2

3a=AD

∴ Each of its altitude=3aunit

Therefore, the altitude of the equilateral triangle is AD=3aunit


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