adjacent corrals

Question

A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 330 yd of fencing is available, find the largest total area that can be enclosed.

 

 

The river runs the length of the corrals. The two corrals share a side so there are three widths and length. 

Answer 1

By guess and check I figured this out:

 

Let x = width and y = length

 

y + 3x = 330, the perimeter

 

Area equals x times y

 

I discovered that if y = 165, then x = 55, and area = 9075.  This was my maximum area solution.  I notice that 165 is 330 divided by 2, but I'm not sure how this fits in.