how to determine if value can represent the side lengths of triangle
To determine if a set of three values can represent the side lengths of a triangle, you need to check if they satisfy the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Here are the steps to determine if a set of values can represent the side lengths of a triangle:
1. Sort the values in ascending order from smallest to largest.
2. Check if the sum of the two smaller values is greater than the largest value. If it is, then the values can represent the side lengths of a triangle. If not, they cannot form a valid triangle.
For example, let's say you have the values 3, 4, and 5. Sorting them in ascending order gives you 3, 4, 5. Now checking the triangle inequality theorem, you see that 3 + 4 = 7, which is greater than 5. Therefore, these values can represent the side lengths of a triangle.
However, if you have the values 2, 3, and 7, sorting them gives you 2, 3, 7. But when you check the triangle inequality theorem, you find that 2 + 3 = 5, which is not greater than 7. Therefore, these values cannot form a valid triangle.