Question

Determine if a right triangle can be formed from the given measurements? Select all that apply.


15in, 19in, 24in


11in, 18in, 21in


7in, 24in, 25in


8in, 15in, 17in


5in, 12in, 13in


12in, 16in, 20in
which ones are correct

Answer 1

To determine if a right triangle can be formed from the given measurements, we will use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true.

We will check each set of measurements:

1. **15 in, 19 in, 24 in:**
\(15^2 + 19^2 = 225 + 361 = 586\)
\(24^2 = 576\)
(Not a right triangle)

2. **11 in, 18 in, 21 in:**
\(11^2 + 18^2 = 121 + 324 = 445\)
\(21^2 = 441\)
(Not a right triangle)

3. **7 in, 24 in, 25 in:**
\(7^2 + 24^2 = 49 + 576 = 625\)
\(25^2 = 625\)
(This is a right triangle)

4. **8 in, 15 in, 17 in:**
\(8^2 + 15^2 = 64 + 225 = 289\)
\(17^2 = 289\)
(This is a right triangle)

5. **5 in, 12 in, 13 in:**
\(5^2 + 12^2 = 25 + 144 = 169\)
\(13^2 = 169\)
(This is a right triangle)

6. **12 in, 16 in, 20 in:**
\(12^2 + 16^2 = 144 + 256 = 400\)
\(20^2 = 400\)
(This is a right triangle)

**Correct sets of measurements for forming a right triangle:**
- 7 in, 24 in, 25 in
- 8 in, 15 in, 17 in
- 5 in, 12 in, 13 in
- 12 in, 16 in, 20 in