CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from CAT Geometry - Triangles. CAT exam is known to test on multiple ideas in the same question, so you should be ready to face them. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. In a triangle if 2 sides a and b are given ,one should be able to say all the possiblities of the third side.

Question 7: △ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?

1. 8
2. 6
3. 9
4. 12

Explanatory Answer

Method of solving this CAT Question from Triangles: Let's start with all the possibilities of sides xy of the triangle.

xz = 12
x,z can be 1, 12 or 2, 6 or 3, 4
Possible triangles
1 - 12 - 12
2 - 6 - 5; 2 - 6 - 6; 2 - 6 - 7
3 - 4 - 2; 3 - 4 - 3; 3 - 4 - 4; 3 - 4 - 5; 3 - 4 - 6.

The question is "△ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?"

Hence, the answer is 9 triangles.

Choice C is the correct answer.