A rectangular plot of land will be bounded on one side by an existing stone wall and on the other three sides by a new fence. This rectangular plot of land is to be enclosed by the stone wall and new fence and then divided into two plots by another piece of fencing joining the midpoints of the section of the stone wall and the opposite side. There is 450 feet of fencing available for the project. What are the dimensions of the rectangular plot with the largest area?

Question

anonymous · Answer

make sense so far?
|dw:1387420126100:dw|

anonymous · Answer

yes

anonymous · Answer

k, 

then we have
450 = 3Y + X

anonymous · Answer

we need to maximize area, so that means we need an equation for area, and we need to derive it, set it equal to zero, and solve for the unknown.

anonymous · Answer

Area = X*Y

if
450=3y+x
then
x=450-3y

plug that into our area equation:
Area = X*Y
Area = (450-3y)*Y
A = 450y-3y^2

now take the derivative of the equation
450y-3y^2

anonymous · Answer

can you do this? or should I show you? I gotta go soon

anonymous · Answer

I got it now! Thanks so much!!!

anonymous · Answer

ur welcome ^_^