Is the triangle with side lengths 5, 12, and 13 a right triangle?

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Multiple Choice

Is the triangle with side lengths 5, 12, and 13 a right triangle?

Explanation:
The main idea is using the Pythagorean theorem to identify a right triangle. In a right triangle, the square of the longest side equals the sum of the squares of the other two sides. Here, the longest side is 13, so check 5^2 + 12^2: that’s 25 + 144 = 169, which matches 13^2 = 169. Because the squares align exactly, the triangle has a right angle between the sides of lengths 5 and 12. It’s also a valid triangle since 5 + 12 > 13. So the description that fits is a right triangle.

The main idea is using the Pythagorean theorem to identify a right triangle. In a right triangle, the square of the longest side equals the sum of the squares of the other two sides. Here, the longest side is 13, so check 5^2 + 12^2: that’s 25 + 144 = 169, which matches 13^2 = 169. Because the squares align exactly, the triangle has a right angle between the sides of lengths 5 and 12. It’s also a valid triangle since 5 + 12 > 13. So the description that fits is a right triangle.

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