A planar frame is made of thin uniform rods. The length of section...

A planar frame is made of thin uniform rods. The length of section AB and EF is ${l}_{1}$ and its coefficient of linear expansion is ${\alpha}_{1}$. The length of section CD is ${l}_{2}$ and its coefficient of linear expansion is ${\alpha}_{2}$. CB and DE are of the same length having coefficient of linear expansion ${\alpha}_{2}$. Points A, B, E and F reside on same line, that is, sections AB and EF overlap. Then the ratio $\dfrac{{l}_{1}}{{l}_{2}}$ for which the distance between end A and end F remains the same at all temperatures is $\dfrac{{\alpha}_{2}}{n{\alpha}_{1}}$ then find the value of $n$.