Question
If triangle ABC has sides measuring 39, 15, and 36, is the triangle a right triangle?
Yes, because 1,521 equals 1,521
No, because 39^2+15^2 is not equal to 36^2
No, because the sum of the squared legs do not equal the square root of the hypotenuse
Yes, because 1,746 equals 1,746
Yes, because 1,521 equals 1,521
No, because 39^2+15^2 is not equal to 36^2
No, because the sum of the squared legs do not equal the square root of the hypotenuse
Yes, because 1,746 equals 1,746
Answers
GPT-4o mini
To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can apply 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 lengths of the other two sides.
1. Identify the longest side: The sides are 39, 15, and 36. The longest side is 39.
2. Apply the Pythagorean theorem: We check if \(39^2 = 15^2 + 36^2\).
Calculating the squares:
- \(39^2 = 1521\)
- \(15^2 = 225\)
- \(36^2 = 1296\)
Now calculate the sum of \(15^2\) and \(36^2\):
- \(15^2 + 36^2 = 225 + 1296 = 1521\)
Since \(39^2 = 1521\) and \(15^2 + 36^2 = 1521\), we find:
- \(39^2 = 15^2 + 36^2\)
This means triangle ABC satisfies the Pythagorean theorem, making it a right triangle.
Based on the provided options, the correct answer would be:
**Yes, because 1,521 equals 1,521**.
1. Identify the longest side: The sides are 39, 15, and 36. The longest side is 39.
2. Apply the Pythagorean theorem: We check if \(39^2 = 15^2 + 36^2\).
Calculating the squares:
- \(39^2 = 1521\)
- \(15^2 = 225\)
- \(36^2 = 1296\)
Now calculate the sum of \(15^2\) and \(36^2\):
- \(15^2 + 36^2 = 225 + 1296 = 1521\)
Since \(39^2 = 1521\) and \(15^2 + 36^2 = 1521\), we find:
- \(39^2 = 15^2 + 36^2\)
This means triangle ABC satisfies the Pythagorean theorem, making it a right triangle.
Based on the provided options, the correct answer would be:
**Yes, because 1,521 equals 1,521**.