document.write( "Question 142358This question is from textbook McDougal littell Math
\n" ); document.write( ": What is the largest possible area of a rectangle with integer side length and a perimeter of 22? \n" ); document.write( "

Algebra.Com's Answer #103635 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let one side = $\"c\"$
\n" ); document.write( "Let the other side= $\"d\"$
\n" ); document.write( "Let area = $\"A\"$
\n" ); document.write( "Let perimeter= $\"P\"$
\n" ); document.write( " $\"A+=+cd\"$
\n" ); document.write( " $\"P+=+2c+%2B+2d\"$
\n" ); document.write( " $\"22+=+2c+%2B+2d\"$
\n" ); document.write( " $\"11+=+c+%2B+d\"$
\n" ); document.write( " $\"d+=+11+-+c\"$
\n" ); document.write( "Now substitute into area formula
\n" ); document.write( " $\"A+=+c%2A%2811+-+c%29\"$
\n" ); document.write( " $\"A+=+-c%5E2+%2B+11c\"$
\n" ); document.write( "This is a parabola that has a peak. I know because
\n" ); document.write( "of the (-) sign in front of $\"c%5E2\"$
\n" ); document.write( "The peak is exactly between the x-intercepts, or at
\n" ); document.write( " $\"c+=+%28-b%29%2F%282a%29\"$ where $\"a+=+-1\"$ and $\"b+=+11\"$
\n" ); document.write( "because the equation is in the form $\"A+=+ac%5E2+%2B+bc\"$
\n" ); document.write( " $\"c+=+%28-11%29%2F%28-2%29\"$
\n" ); document.write( " $\"c+=+11%2F2\"$
\n" ); document.write( " $\"P+=+2%2811%2F2%29+%2B+2d\"$
\n" ); document.write( " $\"22+=+11+%2B+2d\"$
\n" ); document.write( " $\"d+=+11%2F2\"$
\n" ); document.write( "So, the max area is
\n" ); document.write( " $\"A%5Bmax%5D+=+%2811%2F2%29%2811%2F2%29\"$
\n" ); document.write( " $\"A%5Bmax%5D+=+121%2F4\"$
\n" ); document.write( " $\"A%5Bmax%5D+=+30.25\"$
\n" ); document.write( " \n" ); document.write( "

\n" );