CAT 2000QA 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).

CAT 2000 QA Q12: What is the number of distinct triangles with integral valued sides and perimeter 14? — Solution | TheCATExam