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

A triangle with sides measuring 3, 4, and 5 is classified as a right triangle because it satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

For the provided side lengths:

• The longest side is 5.

• The squares of the other two sides are 3² = 9 and 4² = 16.

Now, calculate the square of the hypotenuse:

5² = 25

When we add the squares of the other two sides, we get:

3² + 4² = 9 + 16 = 25

Since the square of the hypotenuse (25) equals the sum of the squares of the other two sides (25), it confirms that the triangle is indeed a right triangle.

This classification indicates that one angle in the triangle measures exactly 90 degrees, distinguishing it from other types of triangles, such as equilateral, where all sides and angles are equal, or isosceles, where at least two sides are equal. A scalene triangle,