# 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 z^{2} = x^{2} + y^{2}

(b)

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

Because the points satisfy Pythagorean Theorem z^{2} = x^{2} + y^{2}

**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 z^{2} = x^{2} + y^{2}.

## 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.