FERMAT 2013 Problem 21

Past Contests FERMAT FERMAT - 2013
, ,
1

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.

Image
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

Answer Choices
A. 143.4
B. 150.0
C. 175.2
D. 162.7
E. 405.0