2022 AMC 12A Problem 3

Problem 3 of 25EasierGeometry Combinatorics

Five rectangles,

A,

B,

C,

D,

and

E,

are arranged in a square as shown below. These rectangles have dimensions

1\times6,

2\times4,

5\times6,

2\times7,

and

2\times3,

respectively. (The figure is not drawn to scale.) Which of the five rectangles is the shaded one in the middle?

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Solution

The five areas are

6,\ 8,\ 30,\ 14,

and

6,

which sum to

64.

So the square is

8\times8.

Placing

C

(

5\times6

) across the top left,

D

(

2\times7

) up the right side,

E

(

2\times3

) in the lower left, and

A

(

1\times6

) along the bottom leaves a central

2\times4

gap, which is exactly rectangle

B.

Thus, the correct answer is B.

Tagged: area · tiling · rectangle