Question
Find the range of possible measures of the third side.
Ask by Patel Fernandez. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The third side must be greater than 7 and less than 63.
Solution
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The Deep Dive
To find the range of possible measures for the third side of a triangle with the other two sides measuring 28 and 35, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides must be greater than the length of the third side.
We can set up the inequalities as follows:
-
→ -
→ (This is always true since side lengths must be positive.) -
→
Combining the valid inequalities, we can deduce:
So, the range of possible measures for the third side is between 7 and 63 (not inclusive).
