Question

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}

Answer 1

All of these sets meet the requirements of the triangle inequality. The sum of any two numbers in the set is greater than the third one. (You really only need to check that the sum of the smallest two is greater than the largest.)

It can help to resolve the numbers that are only indicated as to value.

√13 ≈ 3.606

2√10 ≈ 6.325

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Your comparisons can be ...

2 + 3 = 5 > 3.606 . . . is a triangle

5 + 5 = 10 > 6.325 . . . . . . is a triangle

5 + 12 = 17 > 15 . . . . . . . . is a triangle