5. Using gray square tiles with a side length of $5 \mathrm{~cm}$, Margita arranged four shapes on paper as shown in the figure. Then she outlined each shape with a red marker to highlight the number 2022 on the paper. Margita's mother believes that the total length of all the outlines is at least $5 \mathrm{~m}$. Is Margita's mother correct? Justify your answer.

![](https://cdn.mathpix.com/cropped/2024_06_03_47603db0a075197c1d6ag-1.jpg?height=211&width=517&top_left_y=2430&top_left_x=313)

## Problems worth 10 points:
5. Using gray square tiles with a side length of $5 \mathrm{~cm}$, Margita arranged four shapes on paper as shown in the figure. Then she outlined each shape with a red marker to highlight the number 2022 on the paper. Margita's mother believes that the total length of all the outlines is at least $5 \mathrm{~m}$. Is Margita's mother correct? Justify your answer.

![](https://cdn.mathpix.com/cropped/2024_05_30_1ae5e90785d026149547g-03.jpg?height=240&width=551&top_left_y=1576&top_left_x=227)

## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_30_1ae5e90785d026149547g-03.jpg?height=228&width=474&top_left_y=1882&top_left_x=243)

The shape of the number two has a perimeter equal to $10+6+8=24$ side lengths of the square tiles, i.e., $24 \cdot 5=120 \mathrm{~cm}$.

1 POINT

![](https://cdn.mathpix.com/cropped/2024_05_30_1ae5e90785d026149547g-03.jpg?height=214&width=626&top_left_y=2263&top_left_x=241)

The shape of the number zero has a perimeter equal to $10+6+6+2=24$ side lengths of the square tiles, i.e., $24 \cdot 5=120 \mathrm{~cm}$.

1 POINT

Since she arranged three shapes of the number two and one shape of the number zero, the total length of the red line is $3 \cdot 120+120=480 \mathrm{~cm}$.

2 POINTS

$5 \mathrm{~m}=500 \mathrm{~cm}$

1 POINT

Margita's mother is not correct because $480<500$.

1 POINT

TOTAL 6 POINTS