# Which of the following sets could be the sides of a right triangle? {2,3, square root 13} {5, 5, 2 square root 10} {5,12,15}

Let us understand the properties of a right-angled triangle in detail.

## Answer: Only the set {2,3, square root 13} could be the sides of a right triangle.

The problem can be solved using the Pythagoras theorem.

**Explanation:**

The Pythagoras theorem states that the length of the hypotenuse (h) of a right triangle is given by the square root of the sum of the squares of perpendicular sides (a and b).

⇒ h^{2 }= a^{2} + b^{2}

So, out of the 3 options only {2,3, square root 13} satisfies the Pythagoras theorem.

As 2^{2} + 3^{2 }= 4 + 9 = 13 = h^{2}

⇒ h^{2 }= 13

⇒ h^{ }= square root 13

Rest of the options are not pythagoran triplets.