Question

Which of these sets of side lengths are Pythagorean triples? Check all that apply.

10, 24, 26
14, 48, 49
9, 12, 16
9, 40, 41
15, 20, 25

Answer 1

Some primitive triples are ...
(3, 4, 5)
(5, 12, 13)
(7, 24, 25)
(9, 40, 41)
One interesting characteristic of these is that the sum of the last two numbers is the square of the first number.

Any multiple of these will be a Pythagorean triple.

Now consider your list.
a) (10, 24, 26) = 2×(5, 12, 13) . . . IS a Pythagorean Triple
b) 2×(7, 24, 25) = (14, 48, 50), so (14, 48, 49) is NOT a Pythagorean Triple
c) 3×(3, 4, 5) = (9, 12, 15), so (9, 12, 16) is NOT a Pythagorean Triple
d) (9, 40, 41) . . . IS a Pythagorean Triple
e) 5×(3, 4, 5) = (15, 20, 25) . . . IS a Pythagorean Triple

The sets of side lengths that are Pythagorean Triples are ...
(10, 24, 26)
(9, 40, 41)
(15, 20, 25)