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I have a rectangle of width $20$ meters, length $50$ meters.

How to draw the divider inside this rectangle into $5$ parts, each part has an area of $​​200m^2$ provided that the total length of the drawn lines inside the rectangle be divided as short as possible.

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Try to optimize this shape. It should be slightly shorter than 80m enter image description here

A second option is to use circular arcs that meet at angles of $120^\circ$, and cut the edge at right angles. It gives a total length around 78.25m enter image description here

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  • $\begingroup$ Looks about 1.2m shorter. $\endgroup$ – almagest Feb 8 '18 at 14:17
  • $\begingroup$ Great; it seems your shape $2$ is optimal solution; my calculations show total length $78.2644...$ m. $\endgroup$ – Oleg567 Feb 13 '18 at 9:32
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I would draw 4 lines of length 20 separated 10 apart.

Don't know how to prove that this is the best.

Note that after three of these have been drawn, what is left is a 20 x 20 square, so the last line can be vertical or horizontal.

This might imply that other arrangements might be better. However, I don't think so.

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The shortest length between tow lines(opposite side of rectangle) is when the drawn line between them is perpendicular to the sides. You have to draw four such lines to divide the area in five parts The total shortest is $4 \times 20=80 m$

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  • $\begingroup$ But the OP does not specify that the parts are rectangular. $\endgroup$ – almagest Feb 8 '18 at 14:04

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