2006 AMC 12A Problem 6

Problem 6 of 25EasierGeometry

The

8 \times 18

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?

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Solution

The two hexagons form a square of area

8 \cdot 18 = 144,

so the square has side

12.

The staircase cut splits the width into three equal horizontal pieces of length

y,

which together span the full width:

y + y + y = 18,

y = 6.

(The two vertical steps each rise

12 - 8 = 4,

building the extra height of the square.) Thus, the correct answer is A.