How can you maximize area of a rectangle given a total perimeter?

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Lucas Ross
Lucas Ross 2016-2-10
评论： Guillaume 2016-2-10
If you have 30 fence panels each with 1 meter width, how should you arrange them to maximize the area of the rectangle? Write a program that does this for you. And the panels cannot be broken, they have to stay whole.

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VIKAS
VIKAS 2016-2-10
Try to make it a square, as square will have the maximum area for the given perimeter. If creating is not possible try to make the sides difference as minimum as possible. So as you mentioned 30 fence are available so the 7.5 would be the best but as we can not broke the fence i half then 7 fence at one side and 8 fence at other side will be the best option for this.

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Torsten
Torsten 2016-2-10
max_area = 0.0;
for k=1:7
a=k;
b=15-k;
area = a*b;
if area > max_area
a_max = a;
b_max = b;
max_area = area;
end
end
Variables a_max and b_max give you the side lengths of the rectangle with maximum area.
Best wishes
Torsten.
  1 个评论
Guillaume
Guillaume 2016-2-10
The loop is a bit overkill:
num_panels = 30;
sides = 1:floor(num_panels/2);
area = sides.*(num_panels - 2*sides)/2;
[~, optimumlength] = max(area)

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