Question

If p units, q units are the lengths of two sides of a triangle, where p and q are integers and p > q, then the third side can be

• A. (p + q) units
• B. (p – q) units
• C. (p + q + 1) units
• D. (p – q + 1) units

Answer 1

The correct option is D (p – q + 1) units


In a triangle, the sum of any two sides is always greater than the third side and the difference of any two sides is always less than the third side.
Therefore, if p and q are the lengths of any two sides of a triangle, then the length of the third side (say k) must satisfy
p – q < k < p + q
Thus, the possible length of the third side is (p – q + 1) units.
Hence, the correct answer is option (d).