To determine if a triangle with side lengths of 3 cm, 4 cm, and 6 cm is a right triangle, we can use the Pythagorean theorem. This theorem 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 our case, we first identify the longest side, which is 6 cm. The other two sides are 3 cm and 4 cm. According to the Pythagorean theorem, we can express this as:
Hypotenuse2 = Side12 + Side22
Substituting the lengths into the equation:
62 = 32 + 42
This simplifies to:
36 = 9 + 16
When we add 9 and 16, we get:
36 = 25
Since 36 does not equal 25, we can conclude that the triangle with side lengths of 3 cm, 4 cm, and 6 cm is not a right triangle.
Furthermore, we can also confirm this by checking if the sum of the squares of the two shorter sides is greater than the square of the longest side. In this case, the sides do not meet the requirement for being a right triangle based on the Pythagorean theorem.
In summary, a triangle with the side lengths of 3 cm, 4 cm, and 6 cm is not a right triangle because it does not satisfy the conditions set by the Pythagorean theorem.