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

5

If the perimeter of the triangle is "p"

let Total possible triangles "t"

if p = even, then t = \(\frac{p^2}{48}\)

if p = odd, then t =  \(\frac{(p + 3)^2}{48}\)

since, 13 is a odd number then,

 ∴ Total possible triangles = \(\frac{(13 + 3)^2}{48}\) = 5