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##### Changing Area, Changing Perimeter

label Mathematics
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Suppose you consider a rectangular floor space of 36 square meters with whole-number side lengths.  Which design has the least perimeter?  Which has the greatest perimeter?  Explain your reasoning.

Apr 15th, 2015

If the length of the floor is x m, then its width is 36/x. The perimeter of the floor is p(x) = 2x + 72/x. Since both the length and the width take whole number values, x is a divisor of 36. The number 36 has the following divisors: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Consider the following table

x             1         2      3       4        6        9         12       18        36

p(x)       74       40     30     26      24     26         30       40       74

We see that the square design 6x6 has the least perimeter 24, whereas the design 1x36 has the greatest perimeter 74.

Apr 15th, 2015

Thank you, it makes much more sense since you detailed the formula.

Apr 16th, 2015

You are welcome. I just used the table because there was only a finite number of options.

Apr 16th, 2015

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Apr 15th, 2015
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Apr 15th, 2015
Sep 24th, 2017
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