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

A triangle with sides of lengths 3, 4, and 5 is classified as a right triangle. This classification can be determined by applying 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.

In this case, the longest side is 5. To verify if it's a right triangle, calculate:

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

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

Since both results are equal (25 = 25), this confirms that the triangle is indeed a right triangle.

The other options don't apply because:

• An equilateral triangle requires all three sides to be of equal length, which is not the case here.

• An isosceles triangle has at least two sides of equal length, which does not fit as all sides here are of different lengths.

• A scalene triangle has all sides with different lengths, which is true in this case, but