Get: (23-3X)*X=40 and: 23-3X.
The solution is X=5.
(The chicken farm is rectangular, 8 meters long and 5 meters wide)
(2) no.
Suppose you can design a chicken farm with an area of 50 square meters. Assume that the length of the wooden fence perpendicular to the wall is y meters.
Get: (23-3Y)*Y=50
3Y^-23Y+50=0
It is easy to get δ = 23-4 * 3 * 50 =-79.
So this equation doesn't hold. You can't design a chicken farm with an area of 50 square meters.