Which are the side lengths of a right triangle? Check all that apply.

3, 14, and StartRoot 205 EndRoot
6, 11, and StartRoot 158 EndRoot
19, 180, and 181
3, 19, and StartRoot 380 EndRoot
2, 9, and StartRoot 85 EndRoot

3, 14, and StartRoot 205 EndRoot

19, 180, and 181

2, 9, and StartRoot 85 EndRoot

Step-by-step explanation:

we know that

In a right triangle, the length sides must satisfy the Pythagorean Theorem

so

where

c is the greater side (the hypotenuse)

a and b are the legs

Part 1) we have

3, 14, and StartRoot 205 EndRoot

we have

substitute

----> is true

Satisfy the Pythagorean theorem

therefore

These are the lengths of a right triangle

Part 2) we have

6, 11, and StartRoot 158 EndRoot

we have

substitute

----> is not true

Not satisfy the Pythagorean theorem

therefore

These are not the lengths of a right triangle

Part 3) we have

19, 180, and 181

we have

substitute

----> is true

Satisfy the Pythagorean theorem

therefore

These are the lengths of a right triangle

Part 4) we have

3, 19, and StartRoot 380 EndRoot

we have

substitute

----> is not true

Not satisfy the Pythagorean theorem

therefore

These are not the lengths of a right triangle

Part 5) we have

2, 9, and StartRoot 85 EndRoot

we have

substitute

----> is true

Satisfy the Pythagorean theorem

therefore

These are the lengths of a right triangle

a

explanation: