To determine which set of numbers could represent the side lengths of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse), the relationship \(a^2 + b^2 = c^2\) must hold.
Let's evaluate each set of numbers provided:
-
4, 8, 12
- \(4^2 + 8^2 = 16 + 64 = 80\)
- \(12^2 = 144\)
- \(80 \neq 144\) (not a right triangle)
-
3, 5, 34
- \(3^2 + 5^2 = 9 + 25 = 34\)
- \(34^2 = 1156\)
- \(34 = 34\) (wrong comparison; only one side matches and no further validation)
-
15, 15, 21
- \(15^2 + 15^2 = 225 + 225 = 450\)
- \(21^2 = 441\)
- \(450 \neq 441\) (not a right triangle)
-
10, 24, 26
- \(10^2 + 24^2 = 100 + 576 = 676\)
- \(26^2 = 676\)
- \(676 = 676\) (matches; this is a right triangle)
Based on this evaluation, the only set of numbers that could represent the side lengths of a right triangle is:
10, 24, 26.