Posted by Lisa on .
We have 900 ft of fencing and we want to construct a back yard. If we are using the building as part of the barrier for the yard what are the dimensions that allow maximum area?
I am not even sure how to start though I know I am supposed to calculate the derivative of the setup. Thank you

Maximum Area 
Steve,
if the yard has dimensions x and y, and side x is parallel to the building, then the fencing used is
x+2y = 900
The area is
a = xy = (9002y)*y = 900y  2y^2
da/dy = 900  4y
da/dy=0 when y=900/4 = 225
so, x = 9002y = 450
the yard is thus 450 by 225 
Maximum Area 
Lisa,
I do not think I made it clear sir. The part where I was stuck was where 100 ft. of the building is covered by the side of the yard.
___________________
 yard 
 

} building {

the building length is 100 feet
Sorry for any confusion this caused. 
Maximum Area 
Lisa,
As the text drawing did not come out clear I hope this may clarify what I meant.
imgur /F5NJVqp 
Maximum Area 
Steve,
You're right  you did not make it clear that the building was only 100 feet wide.
If the building on;y covers 100 feet of the side x, then
x+(x100)+2y = 900
2x+2y=1000
x = 500y
and follow the same steps above.
If I still have it wrong, then just draw yourself a diagram and label the various parts, making sure all the fence sections add up to 900. Then substitute for x or y in the formula a=xy.