To determine whether a triangle with side lengths of 3 cm, 4 cm, and 6 cm is a right triangle, we can use 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 6 cm. We check the relationship as follows:
62 = 36
32 + 42 = 9 + 16 = 25
Since 36 is not equal to 25, the triangle does not satisfy the Pythagorean theorem. Therefore, the triangle with side lengths of 3 cm, 4 cm, and 6 cm is not a right triangle.