The perimeter of a triangle with sides of integer values is equal to 13. How many such triangles are possible?

Solution (By Examveda Team)

Number of possible triangles when perimeter is odd
$$\eqalign{ & = \frac{{{{\left( {P + 3} \right)}^2}}}{{48}} \cr & = \frac{{{{\left( {13 + 3} \right)}^2}}}{{48}} \cr & = \frac{{16 \times 16}}{{48}} \cr & = \frac{{16}}{3} \cr & = 5\,... \cr & = 5 \cr} $$