Answer
The length of the brick as measured by the rule would be $24.98~cm$
Work Step by Step
We can find the increase in the length of 25.00 cm of the steel rule when it is heated:
$\Delta L = \alpha~\Delta T~L$
$\Delta L = (12\times 10^{-6}~K^{-1})(60.00~K)~(25.00~cm)$
$\Delta L = 1.80\times 10^{-2}~cm$
The new length of the section of the steel rule marked as 25.00 cm is $25.00~cm+1.80\times 10^{-2}~cm$ which is $25.018~cm$
We can find the increase in length of the brick when it is heated:
$\Delta L = \alpha~\Delta T~L$
$\Delta L = (7.5\times 10^{-7}~K^{-1})(60.00~K)~(25.00~cm)$
$\Delta L = 1.125\times 10^{-3}~cm$
The new length of the brick is $25.00~cm+1.125\times 10^{-3}~cm$ which is $25.001125~cm$
We can find the length of the brick as measured by the rule:
$\frac{25.001125~cm}{25.018~cm}\times (25.00~cm) = 24.98~cm$
The length of the brick as measured by the rule would be $24.98~cm$
