Question 608493
<pre><b>
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?  <font color = "blue">Using the smallest possible perimeter</font>, 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</pre>