Optimizing Boom Length for Oil Spill Containment: A Calculus Approach

[sweet877]

To contain oil spills, rectangular booms that have a cross-link to provide stability are used. The cross-link joins the long sides and is parallel to the short sides. What is the minimum total length of boom required to enclose an oil spill covering 100 000 m^2 of water if it can only be constructed from 10-m sections?

I figured out how to do this if 10-m sections are not required, but cannot figure out what to do if the booms have restrictions. Please advise. Thanks!

 

[HallsofIvy]

What length and width do you get if 10-m sections are not required? What are the closest multiples of 10 larger than that?

 

[sweet877]

250 m and 400 m. But I just got that from common sense. Is there a "calculus way" to do it?