Difference between revisions of "2006 AMC 10A Problems/Problem 7"
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== Solution == | == Solution == | ||
− | Since the two hexagons are going to be repositioned to form a square without overlap, the area will remain the same. The rectangle's area is 18*8=144. This means the square will have four sides of length 12. | + | Since the two hexagons are going to be repositioned to form a square without overlap, the area will remain the same. The rectangle's area is 18*8=144. This means the square will have four sides of length 12. The only way to do this is shown below. |
+ | [[Image:Square.jpg]] | ||
== See Also == | == See Also == | ||
*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] |
Revision as of 14:26, 18 July 2006
Problem
Missing diagram
The rectangle
is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is
?
Solution
Since the two hexagons are going to be repositioned to form a square without overlap, the area will remain the same. The rectangle's area is 18*8=144. This means the square will have four sides of length 12. The only way to do this is shown below. File:Square.jpg