A unit scale is to be prepared whose length does not change with...

Linear expansion of solid with temperature is given by ${L}_{f} = {L}_{0}\left(1 + \alpha ∆ T\right)$

Here, ${l}_{B}\left(1 + {\alpha}_{B}\DeltaT\right) - {l}_{i}\left(1 + {\alpha}_{i}\DeltaT\right) = {l}_{B} - {l}_{i}$

$⇒ {\alpha}_{B}{l}_{B} = {l}_{i}{\alpha}_{i}$

$⇒ 1 . 8 \times {10}^{- 5} \times 40 = {l}_{i} \times 1 . 2 \times {10}^{- 5}$

$⇒ {l}_{i} = \dfrac{1 . 8 \times {10}^{- 5} \times 40}{1 . 2 \times {10}^{- 5}} = \dfrac{3 \times 40}{2} = 60$

$⇒ {l}_{i} = 60cm$