Q. 2 A4.3( 22 Votes )

# Solve the following examples.Find the height of an equilateral triangle having side 2a.

Let ABC be an equilateral triangle,

Let AP be a perpendicular on side BC from A.

To find : Height of triangle = AP

As, ABC is an equilateral triangle we have

AB = BC = CA = 2a

Also, we know that Perpendicular from a vertex to corresponding side in an equilateral triangle bisects the side

Now, In ΔABP, By Pythagoras theorem

(Hypotenuse)2 = (base)2 + (Perpendicular)2

AB2 = BP2 + AP2

(2a)2 = a2 + AP2

AP2 = 4a2 - a2

AP2 = 3a2

AP = a3

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