The sides of a triangle are in Arithmetic Progression $(A.P.).$ If the smallest angle of the triangle is $\alpha$ and largest angle of the triangle exceeds smallest angle by $\beta$ , then what is the perimeter of the triangles.
Is it possible to find the perimeter here with the given data?
No...you can get any perimeter you like. To see this: take any triangle of the form you want. Take, for example, the triangle with sides $\{2,3,4\}$. Any triangle similar to that has the same property, as $\{2\lambda,3\lambda,4\lambda\}$ is still in arithmetic progression, but they all have the same angles.