Answer:
Step-by-step explanation:
We can test these numbers to see if they satisfy the Pythagorean theorem equation:
15² = 9² + 12²
225 = 81 + 144 . . . . true
Since the numbers satisy the Pythagorean theorem relation, they belong to a right triangle.
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You can recognize that the ratio of side lengths is ...
9 : 12 : 15 = 3 : 4 : 5
Further, you can recognize that the side lengths 3, 4, 5 belong to the right triangle with the smallest integer side lengths that satisfy the Pythagorean theorem. Hence the 9 : 12 : 15 triangle is similar (by a scale factor of 3) to a right triangle, thus is a right triangle.
