mechanics 2 problem

hi. hope someone can help with this question...........

A string of natural length 2a and modulus of elasticity 'lambda' has its ends attached to fixed points A and B on a smooth horizontal table, where AB = 3a. Find the work done when the midpoint C of the string is pulled away from the line AB to a position where triangle ABC is equilateral.

Been trying this for hours, going all places except the given solution (15/4)'lambda'*a.

i have calculated the overall tension in the string as (3/2)lambda when it is in the position where ABC is quadrilateral. I have then resolved this in the perpendicular direction to get the force (3root3/4)lambda and tried to do force x distance. doesnt seem to work.......anyone know the correct path?? thanks.

This won't work because the force gradually increases as you stretch the string. WD = force x distance is only true for a constant force.

Instead find the increase in elastic potential energy of the string.

Work done = elastic energy at the end - elastic energy at the beginning (remember that the string was already stretched when you started).