If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

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A triangle with sides of lengths 3, 4, and 5 is classified as a right triangle. This classification is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the sides of the triangle can be labeled as follows: the lengths 3 and 4 are the two shorter sides, and the length 5 is the longest side. To check if this triangle is a right triangle, we calculate:

  • The square of the longest side: (5^2 = 25)

  • The sum of the squares of the other two sides: (3^2 + 4^2 = 9 + 16 = 25)

Since (25 = 25), the sides satisfy the Pythagorean theorem, confirming that the triangle is indeed a right triangle.

Thus, the correct choice reflects the properties of these specific side lengths, demonstrating a fundamental aspect of triangle classification based on geometry.

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