6751
/www/nrich/html/content/id/6751/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">
<br></br>
<p>Tom and Jerry started with identical rectangular sheets of paper. Each of them cut his sheet into two. Tom obtained two rectangles, each with a perimeter of $40$cm while Jerry obtained two rectangles, each with a perimeter of $50$cm. What was the perimeter of Tom's original sheet of paper?<br></br>
<br></br>
If you liked this problem, <a href="http://nrich.maths.org/public/viewer.php?obj_id=4889&part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p>
<p> </p>
<p> </p>
</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>Tom and Jerry must each cut their piece of paper in half. Suppose the sides of the original piece of paper have length $2x$ and $2y$, with $x\geq y$.<br></br>
<br></br>
<mdo:image alt="" height="227" src="recs.jpg" width="405"></mdo:image><br></br>
Then $2x+4y=40$ and $4x+2y=50$ which implies that $6x+6y=90$, therefore the perimeter of the original piece, $4x+4y=60$.<br></br>
</p></mdoxml>
2
3
0
0
1
0
0
Weekly Problem 50 - 2009
Measures and Mensuration
Perimeters