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

Answer: Option A

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