Tension problem

1. The problem statement, all variables and given/known data

A particle P of mass m is suspended from two strings AP and BP where A and B are attached to 2 points on a horizontal ceiling distance 5l/4 apart as shown in the figure. AP is inelastic and of length l. The modulus of elasticity of BP is λ. Show that the natural length L is given by L= 5λl/3mg+5λ
3. The attempt at a solution
Here the mass attached at the point P is in equilibrium which means that the vertical components of the tension caused in AP and BP nullify the weight acting downward. What I am finding difficult to grasp is the fact that the string AP is inelastic and rigid and how it’s rigidity affects the tension since there will be no extension in AP. It would be really helpful if any of you could drop a hint as to how I can establish a relation between the tension of AP and that of BP and if they are equal by any chance???

Attached Images
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