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}

Solution:

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).

⇒ h² = a² + b²

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

As 2² + 3² = 4 + 9 = 13 = h²

⇒ h² = 13

⇒ h =  √13

Rest of the options are not pythagoran triplets.

Thus, only the set {2, 3, square root 13} could be the sides of a right triangle.

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}

Summary:

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