10 Rope Border
10 Rope Border
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please help me!!!!!! 10 POINTS! 
hard math question.?
we're doing this in our unit in calc with 1st/2nd derivatives, intervals etc etc
A park ranger has 600m of floating rope. she is going to enclose a rectangular swimming area, using the beach as one border of the area. find the maximum area that can be enclosed and the corresponding dimensions.
answer is : 45,000m^2 ; 150m x 300m
PLEASE SHOW WORK
Think about what you know and what must be true. Imagine l = the length along the beach that forms one boundary. So,
600 = l + 2d, where d = the distance from the beach for the rectangular area.
Now, recognize that the area is:
A=(l)(2d)
Replace l in this equation by a relationship for the rope distance from above
600 = l + 2d
l = 600-2d
A = (600-2d)(2d)
A = 1200d - 4d^2
Solve for maximum Area by taking dA/dd:
dA/dd = 1200-8d
Solve this by setting it equal to zero for the maxima:
0 = 1200 - 8d
d = 1200/8
d = 150
so if 600 = 2d +l, then l = 300.
Now solve for the area, A = (150m)(300m) = 45,000 m^2
Always start these types of problems with a picture in your mind or on the paper, and represent the equations with what you are given. You'll do fine on the test!