Christmas Cut-Out
Weekly Problem 52 - 2017
Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?
Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?
Age
11 to 14
Challenge level
Problem
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She cuts out ten squares, each measuring $5\text{cm}$ by $5\text{cm}$ from the rectangle to make a Christmas decoration.
In each case, exactly one side of the square lies along a side of the rectangle, and none of the cut out squares touch or overlap.
What is the perimeter of the Christmas decoration?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
The original rectangle had a perimeter of $2 \times 30\text{cm} + 2\times 40\text{cm} = 140\text{cm}$.
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This means the overall effect of cutting out each square is to increase the perimeter by $10\text{cm}$. Since are ten squares, the overall increase is $10 \times 10 \text{cm} = 100\text{cm}$.
Therefore the final perimeter is $140\text{cm} + 100\text{cm} = 240\text{cm}$.