find values for r and t such that the inequality r < S < t best describes s, the length of the third sides of a triangle for which the lengths of the other two sides are given.
11. 2 and 4
thanks for the help !
To find values for r and t that best describes the length of the third side of a triangle (s), given the lengths of the other two sides (S):
1. Start by understanding 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.
2. In this case, we have values of S = 2 and t = 4. We need to find a value for r that satisfies the condition r < S < t.
3. Since S = 2, we need to find a value of r that is less than 2 to ensure r < S. Let's say r = 1.
4. Now, we need to check if r < S and S < t hold true for the given values. In this case, r = 1 < S = 2, so the condition r < S is satisfied.
5. For the condition S < t, we have S = 2 and t = 4. Since 2 < 4, the condition S < t is satisfied as well.
6. Therefore, the values r = 1 and t = 4 satisfy the inequality r < S < t and best describe the length of the third side of the triangle, given that S = 2.
Remember that in different scenarios, the values for r and t may vary, but they should always satisfy the conditions r < S and S < t to describe the length of the third side of the triangle.