Discussion

Explanation:

In a triangle with sides a, b and c, sum of any two sides is greater than the third side, i.e. a + b > c.

∴ For any three sides given, a triangle can be constructed only if sum of any two sides is greater than the third side.

It is given that, a + b + c = 14

Also, it is given that a, b, c are integers.

Case 1: The largest side is 6.
The possible combination of sides is (6, 4, 4), (6, 5, 3) and (6, 6, 2)

Case 2: The largest side is 5.
The possible combination of sides is (5, 5, 4)

∴ The possible sets are (4, 4, 6), (5, 5, 4), (6, 5, 3) and (6, 6, 2).

∴ Only 4 such triangles are possible.

Hence, option (c).

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