Help with writing an Equation for area?

Question

You have 240 feet of wooden fencing to form two adjacent rectangular corrals. You want each corral to have an area of 1000 square feet. So far I have a drawing of a large rectangle, split by a line directly down the middle. This makes the 2 corrals with 4 lines representing length (the horizontal lines), and 3 representing width (the vertical lines). The equation for the perimeter of the entire corral is 4l + 3w = 240, and the equation for the area is (2L)(W) = 2000, or for each individual box it's LW = 1000. How would I write an equation for the area in terms of L? Also, how would you determine the possible dimensions of each corral by completing the square? Thanks.

Answer 1

You have two equations and two unknowns. How do you solve that? (The third equation is useless because it's just the second equation multiplied by two)

Answer 2

Each corral has dimensions $ab$. There is an interior partition (length = b) shared by both corrals. So the total length of fencing $4a+3b=240$. Also, the area of one corral is $ab=1000$.
$4a+3b=240$
$ab=1000$
The top equation is a simple linear Diophantine equation with solution
$a=3c$ and $b=80-4c$.
Substitute these expressions into the bottom equation. This yields a quadratic equation in $c$. Solve it for $c$ and discard the negative value. Substitute the positive value of $c$ into the $c$-expressions for $a$ and $b$. Et voilà!
$a=30+5\sqrt6$
$b={{120-20\sqrt6}\over3}$