If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 13
III. 15
Answers
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III
The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   i.e let us assume the third side be c and other sides be a and b, then as per rule   c &gt; a - b and c &lt; a + b.   Let's take options   option 1. the three sides will be 5 , 4 and 11..   then 11 &gt; 5-4 --Yes   11 &lt; 4+9...NO   option 2... 13, 4 and 11.   then 13 &gt; 11-4...Yes   13 &lt; 11+4...Yes   Option 3..15 ,4 and 11.   15 &lt; 11+4...No   15 &gt; 11-4...Yes...   Only 13 is correct .   Answer: option II only is correct..
<result>B</result>
If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 13
III. 15