Question: How many triangles with integral valued sides can be formed having perimeter 14 units?
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).