## Task 1 - 210611

For a rectangle, the following properties are known:

If its two side lengths are measured in meters, the measurement values are natural numbers. The difference between the two side lengths is $20 \mathrm{~m}$. The perimeter of the rectangle is $60 \mathrm{~m}$.

a) What is the area of this rectangle?

b) What are the lengths of its two sides at a scale of $1: 250$?

Draw the rectangle at this scale!
a) If the larger side length of the rectangle is reduced by $20 \mathrm{~m}$, its perimeter decreases by 40 $\mathrm{m}$, reaching a value of $20 \mathrm{~m}$. At the same time, a square is formed.

Since 20: $4=5$, the side length of the square is $5 \mathrm{~m}$; this is also the length of the shorter side of the original rectangle. The length of its longer side is therefore $25 \mathrm{~m}$. Since $5 \cdot 25=125$, the area of the rectangle is $125 \mathrm{~m}^{2}$.

b) On a scale of 1 : 250, since $5 \mathrm{~m}=500 \mathrm{~cm}$ and 500 $: 250=2$, the shorter side length is represented by a side length of 2 $\mathrm{cm}$. Since $25 \mathrm{~m}=2500 \mathrm{~cm}$ and $2500: 250$ $=10$, the longer side length is represented by a length of $10 \mathrm{~cm}$.