## Task 2 - 340622

The gardens of the Kniffel family and the Knobel family are both square-shaped and adjoin each other as shown in Figure a.

The area of Kniffel's garden is 1225 square meters, and the area of Knobel's garden is 625 square meters.

a) What is the width $A D$ or $E F$ of the gardens?

b) The Kniffel family gives a piece of their garden to the Knobel family. After this, both gardens have the same area. How large is this area?

c) Figure b shows the new division. By what length $G H$ has Knobel's garden become longer?
a)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0294.jpg?height=345&width=465&top_left_y=1455&top_left_x=544)
b)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0294.jpg?height=337&width=462&top_left_y=1459&top_left_x=1094)
(a) Since $35 \cdot 35 = 1225$, a square with a side length of $35 \, \text{m}$ has an area of 1225 square meters. Therefore, the width of Kniffel's garden $AD = 35 \, \text{m}$. From $25 \cdot 25 = 625$, it follows that $EF = 25 \, \text{m}$.

(b) Since $1225 + 625 = 1850$, the two gardens together have 1850 square meters. After dividing into two equal areas, each has $1850 \div 2 = 925$ square meters.

(c) In the rectangle $KEFH$ with this area and the side length $EF = 25 \, \text{m}$, the other side length $FH = 37 \, \text{m}$ because $925 \div 25 = 37$.

Thus, $GH = FH - FG = 37 \, \text{m} - 25 \, \text{m} = 12 \, \text{m}$.