Question

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?

$A$

$B$

$C$

$D$

$E$

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.

2022 AMC 12A Problem 3

Solution:

Problem 3 in Other Years