Rectangle Cutting
Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?
Age
14 to 16
Challenge level
Problem
Tom and Jerry started with identical rectangular sheets of paper. Each of them cut his sheet in half. 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?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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 $x\geq y$.
Image
Then $2x+4y=40$ and $4x+2y=50$ which implies that $6x+6y=90$, therefore the perimeter of the original piece, $4x+4y=60$.