You are the manager of a band that has been hired to perform at a party, and you want to create the largest dance floor possible for the attendees. You have 100 yards of rope to delineate the space, but you do not have to put rope on the side next to the stage. How can you make the most of your space?

Question

anonymous · Answer

the hidden assumption here is that you need a rectangle right?  otherwise you would make a semicircle

anonymous · Answer

is this a calculus question or an algebra question?  by which i mean, are you supposed to use algebra or calculus?

anonymous · Answer

precalculus

anonymous · Answer

ok then before we begin lets say what the answer is. 
use half of the rope for the side opposite the stage, and the rest spit evenly between the other two sides

if you had to use all four sides you would make a square, but if you get one side free that is the answer

anonymous · Answer

here is the work: call the sides adjacent to the stage $x$ then since you have 100 feet of rope the side opposite the stage must be $100-2x$

area is therefore $A(x)=x(100-2x)=100x-2x^2$|dw:1347243290942:dw|