By definition, if two figures are similar, then their corresponding angles have the same measure and the length of their corresponding sides are in the same ratio.
In this case, you know that the new garage and the current garage are similar. Then, using the information given in the exercise you can set up the following proportion (Where "l" is the length in feet of the new garage):
[tex]\frac{24}{18}=\frac{l}{24}[/tex]Solving for "l", you get:
[tex]\begin{gathered} (24)(\frac{24}{18})=l \\ \\ \frac{576}{18}=l \\ \\ l=32 \end{gathered}[/tex]Since you need to stake and rope off where the concrete will be poured, you need to find the perimeter of the rectangle, in order to calculate the amount of rope (in feet) you are going to need.
Knowing the length and the width of the new garage, you get that its perimeter is:
[tex]\begin{gathered} P=2(32ft)+2(24ft) \\ P=64ft+48ft \\ P=112ft \end{gathered}[/tex]The answer is: Third option.