Given the following set of expressions represent the lengths of the sides of a triangle, find the range of possible values of n.If n + 2, 5, and 9 represent the lengths of the sides of a triangle then Blank 1 Question 22 n Blank 2 Question 22 .
Question
Given the following set of expressions represent the lengths of the sides of a triangle, find the range of possible values of n.If n + 2, 5, and 9 represent the lengths of the sides of a triangle then Blank 1 Question 22 n Blank 2 Question 22 .
Solution
In order for the three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This gives us three inequalities:
- n + 2 + 5 > 9
- n + 2 + 9 > 5
- 5 + 9 > n + 2
Solving these inequalities:
- n + 2 + 5 > 9 simplifies to n > 2
- n + 2 + 9 > 5 simplifies to n > -6
- 5 + 9 > n + 2 simplifies to n < 12
So, the range of possible values for n is 2 < n < 12.
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