The length of the three sides of a right-angled triangle are (x-1)cm, (x+1) cm and (x +3) cm, respectively. The hypotenuse of the right-angled triangle (in cm) is :

10

Here, (x + 3) is greater than the other sides for each value for x

We can take (x + 3) as the hypotenuse

So, \( {(x + 3) }^{2 } \) = \( {(x + 1) }^{2 } \) + \( {(x - 1) }^{2 } \)

⇒ \( {x }^{2 } \) + 6x + 9 = 2(\( {x }^{2 } \) + 1)

⇒ \( {x }^{2 } \) + 6x + 9 = 2\( {x }^{2 } \) + 2

⇒ 2\( {x }^{2 } \) - \( {x }^{2 } \) - 6x + 2 - 9 = 0

⇒ \( {x }^{2 } \) - 6x - 7 = 0

⇒ \( {x }^{2 } \) - 7x + x - 7 = 0

⇒ x(x - 7) + 1(x - 7) =  0

⇒ (x + 1)(x - 7) = 0

⇒ x + 1 = 0

⇒ x = -1 ('-' will be neglected)

⇒ x - 7 = 0

⇒ x = 7

Then, the value of (x + 3) = (7 + 3)cm = 10 cm

Therefore, the hypotenuse of the right angled triangle is 10 cm.