To determine which set of lengths could be the side lengths of a right triangle, we need to use the Pythagorean Theorem. The theorem states that, for a right triangle with side lengths \(a\), \(b\), and hypotenuse \(c\):
\[a^2 + b^2 = c^2\]
Let's check each set of lengths:
1. **20 cm, 22 cm, 29 cm**
\[20^2 + 22^2 = 400 + 484 = 884\]
\[29^2 = 841\]
Since \(884 \ne 841\), this set does not form a right triangle.
2. **10 ft, 12 ft, 15 ft**
\[10^2 + 12^2 = 100 + 144 = 244\]
\[15^2 = 225\]
Since \(244 \ne 225\), this set does not form a right triangle.
3. **7 km, 24 km, 28 km**
\[7^2 + 24^2 = 49 + 576 = 625\]
\[28^2 = 784\]
Since \(625 \ne 784\), this set does not form a right triangle.
4. **13 in, 84 in, 85 in**
\[13^2 + 84^2 = 169 + 7056 = 7225\]
\[85^2 = 7225\]
Since \(7225 = 7225\), this set does form a right triangle.
Therefore, the set **13 in, 84 in, 85 in** could be the side lengths of a right triangle.
3 of 53 of 5 Items Question Which set of lengths could be the side lengths of a right triangle? (1 point) Responses 20 cm, 22 cm, 29 cm 20 cm, 22 cm, 29 cm 10 ft, 12 ft, 15 ft 10 ft, 12 ft, 15 ft 7 km, 24 km, 28 km 7 km, 24 km, 28 km 13 in, 84 in, 85 in
1 answer