Bot GPT 4-o mini To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the sum of the squares of the two shorter sides (the legs) equals the square of the longest side (the hypotenuse).
First, we identify the longest side among the three given lengths. The sides are:
- 39
- 15
- 36
The longest side is 39, so we will consider it as the hypotenuse.
Now, we can apply the Pythagorean theorem:
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The sum of the squares of the two other sides: \[ 15^2 + 36^2 = 225 + 1296 = 1521 \]
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The square of the longest side (hypotenuse): \[ 39^2 = 1521 \]
Since \(15^2 + 36^2 = 39^2\), we can conclude that:
Yes, triangle ABC is a right triangle because \(1,521 = 1,521\).
The correct response is: Yes, because 1,521 equals 1,521.
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