Answer:
a = 3, b = 4, and c = 5.
Explanation:
The number of possible triangles that can be formed given three sides, a, b, and c, is determined by the triangle inequality theorem. According to this theorem, the sum of any two sides of a triangle must be greater than the length of the third side. To determine the number of possible triangles, you can follow these steps: 1. Identify the three given side lengths, a, b, and c. 2. Check if the sum of any two sides is greater than the length of the third side. For example, if a + b > c, a + c > b, and b + c > a, then a triangle can be formed. 3. Count the number of valid combinations that satisfy the triangle inequality theorem. Each valid combination represents a possible triangle. 4. If there are no valid combinations, then no triangle can be formed. Let's consider an example: Suppose we have the side lengths a = 3, b = 4, and c = 5. Using the triangle inequality theorem, we check if the sum of any two sides is greater than the length of the third side: a + b = 3 + 4 = 7 > c a + c = 3 + 5 = 8 > b b + c = 4 + 5 = 9 > a Since all three conditions are satisfied, a triangle can be formed. Therefore, there is one possible triangle that can be formed with side lengths a = 3, b = 4, and c = 5.