Which of the following sets could be the sides of a right triangle?
{2, 3, √10}, {3, 5, √34}, {5, 8, 12}

Solution:

If x, y are the two sides and z is the hypotenuse of a right angle triangle then the points should satisfy Pythagorean Theorem.

(a)

The points 2, 3, √10 are not the three sides of a right angle triangle.

Because the points does not satisfy Pythagorean Theorem z² = x² + y²

(b)

The points 3, 5, √34 are the three sides of a right angle triangle.

Because the points satisfy Pythagorean Theorem z² = x² + y²

Verification:

(√34)² = 34 (root and square cancels)

(5)² + (3)² = 25 + 9 = 34

Therefore, 

(√34)² = (5)² + (3)²

(c)

The points 5, 8, 12 are not the three sides of a right angle triangle.

Because the points do not satisfy Pythagorean Theorem z² = x² + y².

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Which of the following sets could be the sides of a right triangle?

Summary:

{3, 5, √34} represents the sides of a right triangle. In a right triangle, the other two angles share the remaining 90 degrees.The right angle has the two sides that are perpendicular to one another.