Which side lengths would form a right triangle?(1 point)Responses9, 12, & 149, 12, & 1421, 16, & 1221, 16, & 1224, 7, & 2624, 7, & 2630, 24, & 18

Answer 1

To determine which side lengths can form a right triangle, we need to check if they satisfy the Pythagorean theorem:

\[ a^2 + b^2 = c^2 \]

where \(c\) is the longest side (hypotenuse) and \(a\) and \(b\) are the other two sides.

Let's check each set of side lengths:

1. 9, 12, & 14:

   • \(14^2 = 196\)
   • \(9^2 + 12^2 = 81 + 144 = 225\) (Not a right triangle)

2. 21, 16, & 12:

   • \(21^2 = 441\)
   • \(16^2 + 12^2 = 256 + 144 = 400\) (Not a right triangle)

3. 21, 16, & 12 (duplicate, already checked)

4. 24, 7, & 26:

   • \(26^2 = 676\)
   • \(24^2 + 7^2 = 576 + 49 = 625\) (Not a right triangle)

5. 24, 7, & 26 (duplicate, already checked)

6. 30, 24, & 18:

   • \(30^2 = 900\)
   • \(24^2 + 18^2 = 576 + 324 = 900\) (This is a right triangle)

So, the side lengths 30, 24, & 18 can form a right triangle.