Question
Question
If triangle ABC
has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point)
Responses
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because 392+152≠362
No, because 39 squared plus 15 squared not equal to 36 squared
Yes, because 1,521 equals 1,521.
Yes, because 1,521 equals 1,521.
Yes, because 1,746 equals 1,746.
Yes, because 1,746 equals 1,746.
Remaining Attempts : 3
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If triangle ABC
has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point)
Responses
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because 392+152≠362
No, because 39 squared plus 15 squared not equal to 36 squared
Yes, because 1,521 equals 1,521.
Yes, because 1,521 equals 1,521.
Yes, because 1,746 equals 1,746.
Yes, because 1,746 equals 1,746.
Remaining Attempts : 3
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Answers
GPT-4o mini
To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
1. Identify the sides: The longest side (which is likely the hypotenuse) is 39, and the other two sides are 15 and 36.
2. Check the Pythagorean theorem:
- Compute the squares of the sides:
- \(39^2 = 1521\)
- \(15^2 = 225\)
- \(36^2 = 1296\)
3. Now, check if \(39^2 = 15^2 + 36^2\):
- \(1521\) (from \(39^2\)) should equal \(225 + 1296\):
- \(225 + 1296 = 1521\)
Since \(39^2 = 15^2 + 36^2\) holds true, triangle ABC is indeed a right triangle.
So the correct response is:
**Yes, because 1,521 equals 1,521.**
1. Identify the sides: The longest side (which is likely the hypotenuse) is 39, and the other two sides are 15 and 36.
2. Check the Pythagorean theorem:
- Compute the squares of the sides:
- \(39^2 = 1521\)
- \(15^2 = 225\)
- \(36^2 = 1296\)
3. Now, check if \(39^2 = 15^2 + 36^2\):
- \(1521\) (from \(39^2\)) should equal \(225 + 1296\):
- \(225 + 1296 = 1521\)
Since \(39^2 = 15^2 + 36^2\) holds true, triangle ABC is indeed a right triangle.
So the correct response is:
**Yes, because 1,521 equals 1,521.**