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

Let ABC is an equilateral triangle of each 2a units

Construction: Draw AD ⊥ BC

Triangles Exercise 6.5 Answer 6

In right ∆ ADB

(AB)= (AD)+ (BD)2

(2a)= (AD)+ (a)2

(4a)= (AD)+ a2

4a– a= (AD)2

3a= (AB)2

√3 a= AD ∴ Each of its altitude= √3 a unit

√3 a = AD

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