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

The only sets of side lengths that are Pythagorean triplets are;

D: 9, 40, 41

E: 15, 20, 25

Pythagorean triplets

Pythagorean triplets is a set of three numbers such that the sum of the last 2 numbers is equal to the square of the first number. Examples are;

(3, 4, 5)

(5, 12, 13)

(7, 24, 25)

(9, 40, 41)

Now, for any of the given options to be regarded as a Pythagorean triplet, then each set must be a factor in the examples of Pythagorean triplets I listed.

From inspection, we can see that;

15, 20, 25 is a factor of (3, 4, 5) because 5(3, 4, 5) = (15, 20, 25)

Finally, (9, 40, 41) is also a Pythagorean triple as given in the examples earlier.

Read More about Pythagorean triplets at; link

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)

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