Question

which set of numbers could represent the side length, in inches, of a right triangle

Answer 1

Answers:
4, 8, 12
3, 5, 34
15, 15, 21
10, 24, 26

Answer 2

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:

1. \(a = 3\)
2. \(b = 4\)
3. \(c = 5\) (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.