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We choose the dance floor with the dimensions of 4x6 for our sister's wedding. We think she would like that size of the dance floor because it gives her plenty of room to get her tango on.

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VA=x=0 The length of the dance floor cannot be 0
SA=y=2x The perimeter cannot be less than twice the length

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As x----> 0 y---->infinity
As x---->infinity y---> 0

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x|| 24  12  8  6  4  3  2  1
y|| 50, 28,22,20,20,22,28,50

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VA=x=0 The dance floor cannot have a length of 0
HA=y=0 The dance floor cannot have a width of 0

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y=24/x

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The 1,24; 2,12; 12,2; and 24;1 all have the most edge pieces.
The 4,6; 6,4 have the least amount of edge pieces.

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As x --> 0 then y--> infinity
As x--> infinity then y--> 0

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x--- 1     2    3 4  6  8  12  24
y---24  12  8  6  4  3   2     1
x=length
y=width

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1x24
2x12
3x8
4x6
6x4
8x3
12x2
24x1

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Problem 9

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We are tasked with creating a dance floor for our sister's wedding. We are are given 24 square tiles to create a rectangular dance floor. Our options for the dance floor are as follows, with the floors length as x and its width as y: (1,24),(2,12),(3,8),(4,6),(6,4),(8,3),(12,2), and (24,1).