2013 Fermat Problem 21

A farmer has a rectangular field with width 45 metres. He divides the field into smaller rectangular animal enclosures in three different sizes, as shown.

Each enclosure labelled A_1 has the same dimensions. Also, the area of the enclosure labelled A_2 is 4 times the area of A_1, and the area of the enclosure labelled A_3 is 5 times the area of A_1. The lines in the diagram represent fences. The total length of all the fences is 360 metres. The area of A_1, in square metres, is closest to

\textbf{(A)}\ 143.4\quad \textbf{(B)}\ 150.0\quad \textbf{(C)}\ 175.2\quad \textbf{(D)}\ 162.7\quad \textbf{(E)}\ 405.0

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.