Final answer:
A triangle with the sides of 6 cm, 8 cm, and 14 cm is possible and it would be an obtuse triangle based on the Triangle Inequality Theorem.
Step-by-step explanation:
Yes, it is definitely possible to form a triangle with the given side lengths of 6 cm, 8 cm, and 14 cm. To determine the type of triangle (whether it's right, acute, or obtuse), we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In addition, if the square of the longest side (in this case, 14 cm) is equal to the sum of the squares of the other two sides (6 cm and 8 cm), then the triangle is a right triangle. In this case, 142 equals 196, while 62 + 82 equals 100, so this is not a right triangle.
If the square of the longest side is greater than the sum of the squares of the two other sides, which is the case here (196 > 100), then the triangle is obtuse. Therefore, a triangle with sides of 6 cm, 8 cm, and 14 cm is an obtuse triangle.
Learn more about Triangle Types