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)![]() ![]() 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 \n" ); document.write( "and will look just the same as \n" ); document.write( "the rectangle with a width of \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( " \n" ); document.write( "So, the rectangle with a \"width\" of \n" ); document.write( "the rectangle with a \"width\" of \n" ); document.write( "the rectangle with a \"width\" of \n" ); document.write( "the rectangle with a \"width\" of \n" ); document.write( "the rectangle with a \"width\" of \n" ); document.write( "The next (and sixth) \"rectangle\" has a \"width\" of \n" ); document.write( "For each rectangle you would calculate \n" ); document.write( " \n" ); document.write( "In square centimeters, the 6 possible areas are: \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \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 \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. \n" ); document.write( " |