Q. 165.0( 1 Vote )

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

Answer :


Given: ABC is an equilateral triangle


AB = AC = BC = 2a


And let AD is an altitude on BC. Therefore,


Now, In ∆ADB, using Pythagoras theorem, we have


(Perpendicular)2 + (Base)2 = (Hypotenuse)2


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


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


(AD)2 = 4a2 – a2


(AD)2 = 3a2


AD = a√3 units


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