Q. 164.2( 6 Votes )

Find the length of the altitude of an equilateral triangle of side 2a cm.

Answer :

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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