Question
The measures of two sides are given. Between what two numbers must the third side fall. 5 and 8
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Answer to a math question The measures of two sides are given. Between what two numbers must the third side fall. 5 and 8
Hank
4.8105 Answers
Solution:
1. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Therefore, the following inequalities must be satisfied:
-a + b > c
-a + c > b
-b + c > a
2. Assign the given side lengths toa b a = 5 b = 8
3. Apply the triangle inequality theorem:
- First inequality:5 + 8 > c c < 13
- Second inequality:c + 5 > 8 c > 3
- Third inequality is redundant asc + 8 > 5 c
4. Therefore, the third side (c
-3 < c < 13
5. Conclusion: The third side must be between 3 and 13.
1. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Therefore, the following inequalities must be satisfied:
-
-
-
2. Assign the given side lengths to
3. Apply the triangle inequality theorem:
- First inequality:
- Second inequality:
- Third inequality is redundant as
4. Therefore, the third side (
-
5. Conclusion: The third side must be between 3 and 13.
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