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

The triangle with side lengths of 3, 4, and 5 can be classified as a right triangle. This classification is confirmed by the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the longest side is 5. To check if it forms a right triangle, we calculate:

3² + 4² = 9 + 16 = 25

And,

5² = 25.

Because both sides of the equation are equal, this confirms that the triangle meets the condition for being a right triangle. Therefore, this triangle is classified as right.

The other types of triangles listed, such as obtuse, acute, and equilateral, do not apply here since an obtuse triangle would require one angle greater than 90 degrees, an acute triangle would have all angles under 90 degrees, and an equilateral triangle would have all sides of equal length. In this case, the specific lengths of 3, 4, and 5 fit only the definition of a right triangle.