CAT Quants | Interesting Geometry Questions

It’s the time of the year to take lots of mocks (around 10 at least)! Carefully analyse and review your mock after taking it, and then proceed to plug in the knowledge gaps! In that interest, here are a few interesting geometry questions for you to take a go at! The detailed solutions for these questions have been provided as well. Happy Solving!

Interesting Geometry Questions:

Here are a few interesting questions on basic concepts from geometry:

1. Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?

2. Triangle ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?

3. Triangle has sides a^2, b^2 and c^2. Then the triangle with sides a, b, c has to be –

a) Right angled

b) Acute-angled

c) Obtuse angled

d) can be any of these three

Interesting Geometry Questions – Solutions

1. Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?

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!

2. Triangle ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?

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
• 3-4-5
• 3-4-6.
• 3-4-4

There are totally 9 triangles.

3. Triangle has sides a^2, b^2 and c^2. Then the triangle with sides a, b, c has to be –

a) Right angled

b) Acute-angled

c) Obtuse angled

d) can be any of these three

Assuming a < b < c, we have a^2 + b^2 > c^2.

This implies the triangle with sides a, b, c has to be acute-angled.

I hope you had fun solving these simple but interesting geometry questions! Here is a wonderful article about CAT Geometry Preparation.

Stay Safe. Best Wishes for CAT!

Rajesh Balasubramanian takes the CAT every year and is a 4-time CAT 100 percentiler. He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.