# The sides of a triangle are $a,b,c$, which are integers, and $a\le b\le c$. If $c$ is given, find the number of triangles possible? [duplicate]

The sides of a triangle are $a$, $b$, and $c$ inches, where $a$, $b$, and $c$ are integers and $a\le b\le c$. If $c$ is given, find the number of triangles possible.

I don't know from where to start this question. Please provide the solution.

## merged by Michael Greinecker♦Jul 11 '18 at 6:36

This question was merged with What is the number of triangles with integer sides, given the length of the longest side? [closed] because it is an exact duplicate of that question.

• This is not really a duplicate of the cited question. That question asks for triangles where $a\le b\color{#C00}{\lt}c$. – robjohn Nov 20 '17 at 12:13