2006 AMC 10A Problems/Problem 7

Revision as of 13:23, 18 July 2006 by Saillsha (talk | contribs) (Solution)

Problem

Missing diagram

The $8x18$ rectangle $ABCD$ 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 $y$?

$\mathrm{(A) \ } 6\qquad \mathrm{(B) \ } 7\qquad \mathrm{(C) \ } 8\qquad \mathrm{(D) \ } 9\qquad \mathrm{(E) \ } 10$

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.

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