Final answer:
To find the range of possible lengths for the third side of a triangle, you can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By setting up inequalities and solving them, you can determine the range of possible lengths.
Step-by-step explanation:
In order to find the range of possible lengths for the third side of a triangle, you need to consider the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, to find the range of possible lengths, you can set up inequalities using this theorem.
For example, let's say you have a triangle with side lengths of 4 cm and 7 cm. To find the range of possible lengths for the third side, you can set up the inequality: 4 + 7 > x, where x is the length of the third side. Simplifying this inequality gives you: 11 > x. So, the third side must be less than 11 cm in order for it to be a triangle.
Similarly, you can set up another inequality using the other two sides of the triangle to find the upper limit of the range of possible lengths. By solving these inequalities, you can determine the range of possible lengths for the third side of a triangle.