Q. 164.2( 6 Votes )
Find the length of the altitude of an equilateral triangle of side 2a cm.
Let ABC be the equilateral triangle whose side is 2a cm.
Let us draw altitude AD such that AD ⊥ BC.
We know that altitude bisects the opposite side.
So, BD = DC = a cm.
In ADC, ∠ADC = 90°.
We know that the Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, by applying Pythagoras Theorem,
AC2 = AD2 + DC2
(2a cm)2 = AD2 + (a cm)2
4a2 cm2 = AD2 + a2 cm2
AD2 = 3a2 cm2
AD = √3 a cm
The length of altitude is √3 a cm.
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