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.

The question invites you to think 'energy stored in a spring' ... so you might try that route. Your idea would work in principle, but notice that the tension isn't constant as you stretch the string and the angle changes as well. Maybe you could work that way but it would be hard and not intended at M2