Which of the following sets of numbers could represent side lengths of a right triangle?
Select one:

15 cm, 18 cm. 33 cm

15 cm, 20 cm, 25 cm

15 cm, 16 cm, 17 cm

15 cm, 15 cm, 18 cm

9514 1404 393

  (b)  15 cm, 20 cm, 25 cm

Step-by-step explanation:

Because you know that the triple (3, 4, 5) is a Pythagorean triple, you know that every multiple of it will also give side lengths of a right triangle. Multiplying that triple by 5 gives (15, 20, 25), matching the 2nd choice on the list.

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Comments on other choices

You also know that (3, 4, 5) is the only Pythagorean triple that has constant differences, so 15, 16, 17 cannot be a right triangle. (It is very nearly an equilateral triangle.)

A right triangle with same-length sides will have a hypotenuse that is √2 times that length, so no right triangle will have two equal integer legs and an integer hypotenuse.

The lengths 15, 18, 33 form a straight line, not even a triangle.

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For those who insist on seeing an equation:

  15^2 +20^2 = 225 +400 = 625 = 25^2 . . . 15, 20, 25 will form a right triangle

y - 25 = 2 ( x - 10 ) should be the answer