What is the number of distinct triangles with integral valued sides and perimeter 14?
Explanation:
Let the sides of the triangle be a, b and c then, a + b > c.
a + b + c = 14
Case 1: Largest side is 6 Possible sets of sides are (6, 4, 4), (6, 5, 3) and (6, 6, 2).
Case 2: Largest side is 5 Possible set of sides is (5, 5, 4).
∴ 4 triangles are possible with integral sides and perimeter 14.
Hence, option (c).
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