CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from CAT Geometry - Triangles. In this problem perimeter of a triangle is given and we have to find out the number of possible triangles. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. Finding perimeter for a triangle whose sides are given is uber-easy. So, why would they ask that? Try the opposite, thats far trickier.

Question 5: Perimeter of a △ with integer sides is equal to 15. How many such triangles are possible?

1. 7
2. 6
3. 8
4. 5

Explanatory Answer

Method of solving this CAT Question from Triangles: This is just a counting question, with the caveat that sum of two sides should be greater than the third.

Let us assume a ≤ b ≤ c.

a = 1, Possible triangle 1, 7, 7
a = 2, possible triangle 2, 6, 7
a = 3, possible triangles 3, 6, 6 and 3, 5, 7
a = 4, possible triangles 4, 4, 7 and 4, 5, 6
a = 5, possible triangle is 5, 5, 5

There are totally 7 triangles possible.

The question is "Perimeter of a △ with integer sides is equal to 15. How many such triangles are possible?"

Hence, the answer is 7.

Choice A is the correct answer.