To solve for the tensions in the strings, we can use the equilibrium conditions for the forces acting on the particle P. The forces involved are the tensions in the strings S₁ and S₂, and the weight of the particle.

Let the tension in S₁ be T₁ and in S₂ be T₂. The weight of the particle is 21 N acting vertically downward.

Using trigonometry, we can resolve the tensions into horizontal and vertical components. The horizontal components must balance each other, and the sum of the vertical components must balance the weight of the particle.

From the diagram, we can determine the angles using the given lengths:

• For S₁: \\(an^{-1}(0.2/0.52) = 21.8^\circ\\)
• For S₂: \\(an^{-1}(0.2/0.25) = 38.7^\circ\\)

Resolving horizontally:

\(T_1 \cos(21.8^\circ) = T_2 \cos(38.7^\circ)\)

Resolving vertically:

\(T_1 \sin(21.8^\circ) + T_2 \sin(38.7^\circ) = 21\)

Solving these equations simultaneously gives:

\(T_1 = 13\) N

\(T_2 = 20\) N