SOLUTION: The new square tiles that I am putting on my kitchen floor have a perimeter of 18 inches. If it takes 384 tiles to cover my rectangular kitchen floor, what is the smallest possibl

The new square tiles that I am putting on my kitchen floor have a perimeter of 18 inches.
If it takes 384 tiles to cover my rectangular kitchen floor, what is the smallest possible
perimeter for my kitchen?  Using the smallest possible perimeter, what is the area of my kitchen?

Suppose the length of the floor is L tile-widths long and
its width is W tile-widths wide, then L×W must equal 384,
and the perimeter will be 2L+2W tile-widths.  Also L and
W must be whole numbers since no tiles were cut. We
want to find the two whole numbers L and W such that
their product LW is 384 and 2L+2W is the smallest 
possible number of tiles.  We will assume that L is
greater than W to save time.  Here are all the
possibilities of whole numbers that have product
384, along with the perimeters, where L > W.

 L            W           P=2L+2W
384           1             770
192           2             388
128           3             262
96            4             200
64            6             140
48            8             112
32            12            88
24            16            80

So the smallest perimeter will be when the floor is
24 tile-widths by 16 tile-widths which has a perimeter of 
80 tile-widths.  You probabably want the answer in feet
rather than in tile-widths though.

Each tile is 18 inches or 1.5 feet wide, so the 
perimeter of 80 tile-widths is 80×1.5 = 120 feet.

That's the answer to the first part.

[The length is 24 tile-widths, and since 24×1.5=36 feet 
the length is 36 feet.  The width is 16 tile-widths and
since 16×1.5=24, the width is 24 feet wide. So the floor
is 36 feet by 24 feet.  That's a large kitchen!]

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The second part has absolutely nothing to do with the 
perimeter, so the words in blue are just to throw you off. 
In fact the answer is 384 tile-areas converted to square 
feet.

Each tile is 18 inches or 1.5 feet wide, so the area
of 1 tile is 1.5×1.5 or 2.25 square feet, so 384 tiles
has an area of 384×2.25 or 864 square feet.

Edwin