Three rods of equal length l are joined to form an equilateral triangle PQR. O is the mid-point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same, i.e. α2 but that for PQ is α1. Then,

(OR)2=(PR)2-(PO)2=l2-l22⇒                   (OR)2=l1+α2t2-l21+α1t2                    l2-l24=l21+α22t2+2α2t-l241+α12t2+2α1tNeglecting α22 t2 and α12 t2 , we get                           0=l22α2t-l242α1t⇒                     2α2 = 2α14⇒                       α1 = 4α2