Question

If 3, 9 and x represent the lengths of the sides of a triangle, possible integer values for x are ___________

• A. the integers that lie less than 6
• B. the integers that lie between 6 and 12
• C. the integers that are above 12
• D. Insufficient data

Answer 1

The correct option is B the integers that lie between 6 and 12

The length of a side must be less than the sum of the other two sides.
Here, that means x < 9+3, or x < 12.
In addition, remember that the length of a side must be greater than the difference of the other two sides.
That means x > 9 - 3, or x > 6.
Therefore we have two limits for the value of x: 6 and 12. 6 < x < 12
Since x is an integer, x can be equal to numbers 7, 8, 9, 10, or 11 (the numbers that lie between 6 and 12 do NOT include 6 and 12).