Question

which set of side lengths can be used to form a right triangle?

30, 40, 50

4, 5, 6

10, 20, 30

2, 3, 4

Answer 1

To determine which set of side lengths can form 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 following relationship holds:

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

Now, let's check each set of side lengths:

1. **30, 40, 50**:
- \(50^2 = 2500\)
- \(30^2 + 40^2 = 900 + 1600 = 2500\)
- This set does satisfy the Pythagorean theorem, so it forms a right triangle.

2. **4, 5, 6**:
- \(6^2 = 36\)
- \(4^2 + 5^2 = 16 + 25 = 41\)
- This set does not satisfy the Pythagorean theorem.

3. **10, 20, 30**:
- \(30^2 = 900\)
- \(10^2 + 20^2 = 100 + 400 = 500\)
- This set does not satisfy the Pythagorean theorem.

4. **2, 3, 4**:
- \(4^2 = 16\)
- \(2^2 + 3^2 = 4 + 9 = 13\)
- This set does not satisfy the Pythagorean theorem.

Only the set **30, 40, 50** can be used to form a right triangle.