## Task 4 - 160514

A rectangular playground is to be fenced. The total length of the fence is $390 \mathrm{~m}$; the long sides of the rectangle are twice as long as the short sides.

a) Determine the side lengths of the playground!

b) Draw the playground (construction of the rectangle) to scale 1 : 1000!
The short side is $a \mathrm{~m}$ long and thus the long side is $b=2 a \mathrm{~m}$ long. For the perimeter of the rectangle, $u=2 a+2 b=2 a+2 \cdot 2 a=6 a=390 \mathrm{~m}$. Therefore, $a=65$.

a) The short sides of the playground are $65 \mathrm{~m}$ and the long sides are $130 \mathrm{~m}$ long.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0073.jpg?height=394&width=780&top_left_y=748&top_left_x=638)

b) In the drawing at a scale of 1 : 1000, the rectangle must be $13 \mathrm{~cm}$ wide and $6.5 \mathrm{~cm}$ high.