Q. 22 D3.5( 8 Votes )

# 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?

Answer :

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

⇒ x^{2} + (x-2)^{2} = (x+2)^{2}

⇒ x^{2} + x^{2} + 4 - 4x = x^{2} +4 +2x

⇒ x^{2}- 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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