# CAT Practice : Geometry - Triangles

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Finding perimeter for a triangle whose sides are given is uber-easy. So, why would they ask that? Try the opposite, thats far trickier.

## Number of triangles

Q.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

Choice (A). 7

## Detailed Solution

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.

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## More questions from Geometry Triangles

Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.