Q. 2 A4.3( 22 Votes )

# Solve the following examples.

Find the height of an equilateral triangle having side 2a.

Answer :

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}

⇒ AB^{2} = BP^{2} + AP^{2}

⇒ (2a)^{2} = a^{2} + AP^{2}

⇒ AP^{2} = 4a^{2} - a^{2}

⇒ AP^{2} = 3a^{2}

⇒ AP = a√3

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