3. A rectangle is composed of 2021 congruent squares, as shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_06_03_93b46e1519bfbf998b64g-2.jpg?height=235&width=951&top_left_y=1533&top_left_x=541)

Determine the perimeter of this rectangle if its area is $18189 \mathrm{~cm}^{2}$.
3. A rectangle is composed of 2021 congruent squares, as shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_30_5cfeb7f7e539b150a939g-08.jpg?height=231&width=968&top_left_y=324&top_left_x=590)

Determine the perimeter of this rectangle if its area is $18189 \mathrm{~cm}^{2}$.

## Solution.

The rectangle is composed of 2021 congruent squares (with side length $a$),

![](https://cdn.mathpix.com/cropped/2024_05_30_5cfeb7f7e539b150a939g-08.jpg?height=140&width=1065&top_left_y=841&top_left_x=264)

so its area is $P=2021 a^{2}$.

$\left.\begin{array}{l}P=2021 a^{2} \\ P=18189 \mathrm{~cm}^{2}\end{array}\right\} \Rightarrow a^{2}=9 \mathrm{~cm}^{2}$

$\Rightarrow a=3 \mathrm{~cm}$

The perimeter of the rectangle is the sum of the lengths of its sides.

![](https://cdn.mathpix.com/cropped/2024_05_30_5cfeb7f7e539b150a939g-08.jpg?height=212&width=1145&top_left_y=1299&top_left_x=250)

Two sides of the rectangle have a length of $a$, and the other two sides have a length of $2021 a$.

The perimeter of the resulting rectangle is calculated as

$o=a+a+2021 a+2021 a=4044 a$.

2 POINTS

After substituting the side length $a=3 \mathrm{~cm}$, we get

$o=4044 \cdot 3 \mathrm{~cm}=12132 \mathrm{~cm}$.

Note: If a student incorrectly determines the side length of the square from the area but correctly calculates the perimeter, 2 POINTS should be deducted.