SOLUTION: A cardboard poster containing 32in^2 of printed region is to have a margin of 2in at the top and bottom and 4/3in at the sides. Create a non-linear function. Represent it in equati

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Question 1067033: A cardboard poster containing 32in^2 of printed region is to have a margin of 2in at the top and bottom and 4/3in at the sides. Create a non-linear function. Represent it in equation and table form.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h+ = height of the printed area
Let +w+ = width of the printed area
Let +A+ = the total area of the poster
------------------------------------
(1) +h%2Aw+=+32+ in2
(2) +A+=+%28+h+%2B+4+%29%2A%28+w+%2B+8%2F3+%29+
Notice I added twice the margins to height and width
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(2) +A+=+h%2Aw+%2B+4w+%2B+%288%2F3%29%2Ah+%2B+32%2F3+
and
(1) +h+=+32%2Fw+
---------------------
(2) +A+=+32+%2B+4w+%2B+%288%2F3%29%2A%2832%2Fw%29+%2B+32%2F3+
(2) +A+=+4w+%2B+256%2F%283w%29+%2B+32+%2B+32%2F3+
---------------------------------------
Here's a plot of this function:

It looks like for +w+=+5+, I get an area of about +80+
+h%2Aw+=+32+
+5h+=+32+
+h+=+32%2F5+
(2) +A+=+%28+h+%2B+4+%29%2A%28+w+%2B+8%2F3+%29+
(2) +A+=+%28+32%2F5+%2B+4+%29%2A%28+5+%2B+8%2F3+%29+
(2) +A+=+%28+52%2F5+%29%2A%28+23%2F3+%29+
(2) +A+=+1196%2F15+
() +A+=+79.73+
Pretty close
Hope this helps -you can make a table
You could also make Area a function of height
instead of width if you wanted to.