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

A triangle with sides of length 3 cm, 4 cm, and 5 cm can be determined to be a right triangle by using 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 other two sides.

In this case, the longest side is 5 cm. To apply the Pythagorean theorem, 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 both calculations equal 25, the conditions of the Pythagorean theorem are satisfied. This confirms that the triangle with sides of length 3 cm, 4 cm, and 5 cm is indeed a right triangle.

The other types of triangles mentioned—inclusive of equilateral, isosceles, and scalene—do not apply to this triangle. An equilateral triangle has all sides equal, an isosceles triangle has at least two sides equal, and a scalene triangle has all sides of