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Coefficient of linear expansion of brass and steel rods are  Lengths of brass and steel rods  respectively. If $\left({l}_{2}-{l}_{1}\right)$ is maintained same at all temperatures, Which one of the following relations holds good?

(a) ${\alpha }_{1}{l}_{2}^{2}={\alpha }_{2}{l}_{1}^{2}$                (b) ${\alpha }_{1}^{2}{l}_{2}={\alpha }_{2}^{2}{l}_{1}$

(c) ${\alpha }_{1}{l}_{1}={\alpha }_{2}{l}_{2}$                (c) ${\alpha }_{1}{l}_{2}={\alpha }_{2}{l}_{1}$

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