Q2 of 45 Page 43

Solve the following examples.

A side of an isosceles right angled triangle is x. Find its hypotenuse.


In a right-angled triangle


By Pythagoras theorem


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


As, the triangle is isosceles


Base = Perpendicular = x


[Hypotenuse can't be equal to any of the sides, because hypotenuse is the greatest side in a right-angled triangle and it must be greater than other two sides]


⇒ (Hypotenuse)2 = x2 + x2


⇒ (Hypotenuse)2 = 2x2


⇒ Hypotenuse = x√2


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