For a set of numbers to represent the side lengths of a right triangle, they must satisfy the Pythagorean theorem, which states that for a right triangle with legs of lengths \(a\) and \(b\), and hypotenuse \(c\), the following must hold true:
\[ a^2 + b^2 = c^2 \]
To form a valid example, let's consider the classic right triangle with side lengths 3, 4, and 5 inches. In this case:
- \(a = 3\)
- \(b = 4\)
- \(c = 5\) (hypotenuse)
Now, we check the Pythagorean theorem:
\[ 3^2 + 4^2 = 9 + 16 = 25 = 5^2 \]
Thus, \(3, 4, 5\) is a valid set of numbers representing the side lengths of a right triangle.
You can generate other sets of side lengths by scaling this triangle or by using other Pythagorean triples, such as:
- \(5, 12, 13\)
- \(7, 24, 25\)
- \(8, 15, 17\)
Any combination of two shorter lengths that satisfies the Pythagorean theorem with one larger length will also represent the side lengths of a right triangle.
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