## Task 1 - 080611

a) The sum of the areas of a rectangular surface and a square surface is $3000 \mathrm{~m}^{2}$. The side of the square and one side of the rectangle have a length of $30 \mathrm{~m}$ each.

a) How long is the other side of the rectangle?

b) Draw both areas to scale $1: 2000$!
Let $a$ be the length of the square sides, $b$ the known, and $c$ the unknown rectangle side. Then (given in meters or square meters):

$$
A_{Q}+A_{R}=a^{2}+b \cdot c \Rightarrow 3000=30^{2}+30 \cdot c \Rightarrow c=70
$$

The unknown rectangle side is $70 \mathrm{~m}$ long.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0180.jpg?height=140&width=577&top_left_y=958&top_left_x=314)

b) see figure. The square side with a length of $30 \mathrm{~m}$ must be $3000 \mathrm{~cm}: 2000=1.5 \mathrm{~cm}$ in the figure.