## Task 1 - 150721

a) A piece of land has the shape of a rectangle, one side of which is $75 \mathrm{~m}$ longer than the other, and the total perimeter is $650 \mathrm{~m}$.

Determine the side lengths and the area (in hectares) of this piece of land!

b) On the entire area of the mentioned piece of land, fruit trees are to be planted in such a way that the trees stand in rows parallel to the sides of the rectangle, i.e., they are not planted "in gaps," and the distance from tree to the next tree and from a side to the nearest tree is $5 \mathrm{~m}$ each.

Determine the exact number of trees that can be planted under the given conditions!
a) If the specifications for a rectangle apply, then the perimeter results from the sum of four times the smaller side length and twice $75 \mathrm{~m}$. Four times the smaller side length thus amounts to $650 \mathrm{~m}-150 \mathrm{~m}=500 \mathrm{~m}$, the smaller side length is therefore $125 \mathrm{~m}$, and the larger side $200 \mathrm{~m}$.

The area of such a rectangle is $125 \cdot 200 \mathrm{~m}^{2}=25000 \mathrm{~m}^{2}=2.5$ ha.

b) According to the conditions of the problem, parallel to the larger side of the rectangle, $\frac{125}{5}-1=24$ and parallel to the smaller side, $\frac{200}{5}-1=39$ trees can be planted. The number of trees sought is thus $24 \cdot 39=936$.