Q2 of 45 Page 43

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 = a√3


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