CAT 2000 — QA Question 12
Basics of TrianglesEasy
What is the number of distinct triangles with integral valued sides and perimeter 14?
Answer & solution
- A
6
- B
5
4
- D
3
Solution
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).