document.write( "Question 242732: This is due in about... 1 hour (at 4oclock for me). I seriously need help or else my teacher will kill me :(\r
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document.write( "Two rectangles have a length and width that are consecutive even integers. The length and width of the larger rectangle are both two inches more than the length and width of the smaller rectangle. If the sum of the perimeters of the two rectangles is at most 64 inches, find the greatest possible perimeter of the larger rectangle. (Hint: Express all dimensions in terms of w, the width of the smaller rectangle.) \n" );
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Algebra.Com's Answer #177688 by solver91311(24713)![]() ![]() You can put this solution on YOUR website! \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Come on now. I don't believe there is any jurisdiction in the world that prescribes capital punishment for the crime of ignorance of mathematics. Personally, I think there are cases where it would be a good idea, but that is another discussion for another time.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "In order to make this work, you have to change the wording of the problem slightly, as follows:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Two rectangles have a length and width measured in inches that are consecutive even integers. The length and width of the larger rectangle are both two inches more than the length and width of the smaller rectangle. If the sum of the perimeters of the two rectangles is at most 64 inches, find the greatest possible perimeter of the larger rectangle.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Otherwise, the length and width could be in centimeters, or Angstroms, or whatever, and then you wouldn't be able to establish a fixed relationship between the smaller and larger rectangles.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Let \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The perimeter of a rectangle is found by:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So now we can write a function for the perimeter of the smaller rectangle as a function of the width of the smaller rectangle:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Using a similar process we can create the function for the perimeter of the larger rectangle, thus:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Then the sum of the perimeters is:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now we know that the sum of the perimeters must be at most 64 inches. That means that:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the largest possible value of \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Evaluate \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Check:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "John \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |