Q. 164.2( 6 Votes )

Find the length o

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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