document.write( "Question 947687: Draw 11 rectangles with a perimeter of 24cm. For the width, use natural numbers, starting at 1. Indicate the length, the width, as well as the area on the sketch of each rectangle \n" ); document.write( "
Algebra.Com's Answer #578339 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
This is a misguided, misleading question, but I think I know how the teacher expects you to interpret it.
\n" ); document.write( "You can choose for the width (in cm) the natural numbers 1, 2, 3, ....,8, 9, 10, and 11, but
\n" ); document.write( "the rectangle with a \"width\" of \"11cm\" will have a \"length\" of \"1cm\"
\n" ); document.write( "and will look just the same as
\n" ); document.write( "the rectangle with a width of \"1cm\" and a length of \"11cm\" .
\n" ); document.write( "I guess what is meant is for you to draw 11 rectangles,
\n" ); document.write( "with a side parallel to left side of the page measuring 1, 2, 3, ... 10, and 11 cm.
\n" ); document.write( "We can call the measure of that side the \"width\".
\n" ); document.write( "Then, we call the measure of a side perpendicular to that one
\n" ); document.write( "(a side parallel to the top edge of the paper) the \"length\",
\n" ); document.write( "without worrying if the \"width\" happens to be more than the \"length\".
\n" ); document.write( "Your drawing could look like this
\n" ); document.write( " Since \"perimeter=2%28width%2Blength%29\" , \"2%28width%2Blength%29=24cm\" ---> \"width%2Blength=24cm%2F2\" ---> \"width%2Blength=12cm\" ---> \"length=12cm-width\"
\n" ); document.write( "So, the rectangle with a \"width\" of \"1cm+\" , will have a length of \"12cm-1cm=11cm\" ;
\n" ); document.write( "the rectangle with a \"width\" of \"2cm+\" , will have a length of \"12cm-2cm=10cm\" ;
\n" ); document.write( "the rectangle with a \"width\" of \"3cm+\" , will have a length of \"12cm-3cm=9cm\" ;
\n" ); document.write( "the rectangle with a \"width\" of \"4cm+\" , will have a length of \"12cm-4cm=8cm\" ;
\n" ); document.write( "the rectangle with a \"width\" of \"5cm+\" , will have a length of \"12cm-5cm=7cm\" , and so on.
\n" ); document.write( "The next (and sixth) \"rectangle\" has a \"width\" of \"6cm+\" , and a \"length\" of \"12cm-6cm=6cm\" . That is a very special kind of rectangle, with the same measure for width and length. That is the kind of rectangle that we commonly call a square.
\n" ); document.write( "For each rectangle you would calculate
\n" ); document.write( "\"area=%28length%29%2A%28width%29\" .
\n" ); document.write( "In square centimeters, the 6 possible areas are:
\n" ); document.write( "\"1%2A11=11\" ,
\n" ); document.write( "\"2%2A10=20\" ,
\n" ); document.write( "\"3%2A9=27\" ,
\n" ); document.write( "\"4%2A8=32\" ,
\n" ); document.write( "\"5%2A7=35\" , and
\n" ); document.write( "\"6%2A6=36\" .
\n" ); document.write( "What your teacher was trying to make you \"discover\" is that
\n" ); document.write( "for any given perimeter, the largest rectangle is a square.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "NOTE: The 7th rectangle would have a with a \"width\" of \"7cm+\" , and a \"length\" of \"12cm-7cm=5cm\" . The measurement that we called \"width\" is greater than the measurement we call \"length\". You may think that the 7th rectangle really has a width of \"5cm\" and a length of \"7cm+\" .
\n" ); document.write( "You may think that the 7th rectangle really is the same rectangle as the 5th rectangle, just aligned in a different direction. The problem with that line of thought is that it leads you to think that there are only 6 possible rectangles instead of 11.
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