Q22 of 99 Page 267

The length of sides of a right-angled triangle are (x – 2) cm, x cm and (x + 2) cm. How much length of hypotenuse is?

In the right angle triangle, hypotenuse is the longest side


In this case, (x+ 2) would be the longest side of the triangle


That would be given by Pythagoras theorem


⇒ x2 + (x-2)2 = (x+2)2


⇒ x2 + x2 + 4 - 4x = x2 +4 +2x


⇒ x2- 6x = 0


⇒ x( x-6) = 0


⇒ x = 0 or x= 6


⇒ Since the side cannot be zero


⇒ x =6


Hence, the hypotenuse = x= 8cm


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