In a triangle, the lengths of the sides are 6 units, 12 units, and x units. How many possible integer values are there for x?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 11.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
6 + 12 > x
⇒ x < 18
6 + x > 12
⇒ x > 6
12 + x > 6
⇒ x > -6
x > 6 and x < 18
The possible integer values of x are 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
Therefore, there are 11 possible integer values for x.