document.write( "Question 1003630: A gardner ordered 60 square slabs measuring 1m by 1m. List different rectangular arrangements? and Find its perimeter and area?
\n" ); document.write( "I have tried solving it. Kindly help is it correct?
\n" ); document.write( "1) 12m long and 5m wide, Perimeter=34m and Area= 60 m-square
\n" ); document.write( "2) 20 m long and 3 m wide, Perimeter= 64m and Area= 60 m-square \n" ); document.write( "

Algebra.Com's Answer #620313 by KMST(5328) $\"\"$ $\"About$

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Those are two of the many possible arrangements, and you correctly calculated the perimeter.
\n" ); document.write( "Th area is 60 square meters for all arrangements of course,
\n" ); document.write( "because the gardener is laying down 60 slabs, each with a 1 square meter surface area.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To find them all, we must list them systematically.
\n" ); document.write( "The width and length of the rectangle (in meters or number of slabs) must divide $\"60\"$ evenly.
\n" ); document.write( "So $\"width\"$ and $\"length\"$ {would be factors of $\"60\"$ such that
\n" ); document.write( " $\"width%2Alength=60\"$ <--> $\"length=60%2Fwidth\"$ .
\n" ); document.write( "We look for small factors of $\"60\"$ that could be the width, and we fond the corresponding length.
\n" ); document.write( "We try 1, 2, 3, etc, in order, and see if each one is a factor.
\n" ); document.write( "It could be:
\n" ); document.write( " $\"width=1\"$ , and $\"length=60%2F1=60\"$ ,
\n" ); document.write( " $\"width=2\"$ , and $\"length=60%2F2=30\"$ ,
\n" ); document.write( " $\"width=3\"$ , and $\"length=60%2F3=20\"$ ,
\n" ); document.write( " $\"width=4\"$ , and $\"length=60%2F4=15\"$ ,
\n" ); document.write( " $\"width=5\"$ , and $\"length=60%2F5=12\"$ ,
\n" ); document.write( " $\"width=6\"$ , and $\"length=60%2F6=10\"$ .
\n" ); document.write( "So we found $\"6\"$ different ways to arrange those $\"60\"$ slabs in a rectangle.\r
\n" ); document.write( "\n" ); document.write( " $\"7\"$ , $\"8\"$ , and $\"9\"$ are not factors (they do not divide $\"60\"$ evenly).
\n" ); document.write( " $\"10\"$ is a factor, but we cannot say that $\"width=10\"$ ,
\n" ); document.write( "because we had already found a rectangle with $\"width=6\"$ , and $\"length=10\"$ above,
\n" ); document.write( "and since the side measuring $\"10\"$ was the longest side,
\n" ); document.write( "it is a length not a width. \n" ); document.write( "

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