If 6, 18, and x are sides of a triangle and x is an integer, then the number of possible values of x is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 11.
We know that,
For any triangle with sides a, b and c
a + b > c, b + c > a and c + a > b
We now have three conditions;
1. 6 + 18 > x
⇒ 24 > x
2. 6 + x > 18
⇒ x > 12
3. 18 + x > 6 (This condition is always true since x is positive)
Combining the three conditions we have
⇒ 12 < x < 24
Possible values of x = 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
Number of possible values = 11