document.write( "Question 1061802: Several rectangles with a perimeter of 14 cm have widths and lengths that are a natural number of centimeters. How many different areas are possible for these rectangles? \n" ); document.write( "

Algebra.Com's Answer #676550 by KMST(5328) $\"\"$ $\"About$

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$\"perimeter=2%28length+%2Bwidth%29\"$
\n" ); document.write( "If $\"2%28length+%2Bwidth%29=14\"$ , $\"length%2Bwidth=14%2F2\"$ ---> $\"length%2Bwidth=7\"$ .
\n" ); document.write( "How many ways can we make $\"length%2Bwidth=7\"$ with natural numbers (the positive integers we use to count)?
\n" ); document.write( "Let us count the ways, starting with $\"width=1\"$ and going wider:
\n" ); document.write( " $\"system%28width=1%2Clength=7-1=6%29\"$ ---> $\"area=6%2A1=6\"$
\n" ); document.write( " $\"system%28width=2%2Clength=7-2=5%29\"$ ---> $\"area=5%2A2=10\"$
\n" ); document.write( " $\"system%28width=3%2Clength=7-3=4%29\"$ ---> $\"area=4%2A3=12\"$
\n" ); document.write( "We cannot say $\"system%28width=4%2Clength=7-4=3%29\"$ is an option,
\n" ); document.write( "because the way we define those words $\"width%3C=length\"$ ,
\n" ); document.write( "and anyway, we would find the same area: $\"area=3%2A4=12\"$ .
\n" ); document.write( "So, there are $\"highlight%283%29\"$ different possible areas. \n" ); document.write( "

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