Rectangle dissection
Weekly Problem 2 - 2009
The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?
The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?
Age
11 to 14
Challenge level
Problem
The 16 by 9 rectangle is cut as shown.
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If the pieces are rearranged to form a square, what is the perimeter of the square?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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The square's perimeter is $12\times 4 = 48$
You could also look at the area of the rectangle. This is $16 \times 9 = 144$. This must be the same as the square, so the square must have side lengths of $12$. Therefore its perimeter is $12 \times 4 = 48$.