Two Gardens

Uncle Ferda had two gardens: the carrot garden was square-shaped, and the strawberry garden was rectangular. The width of the strawberry garden was three times smaller than the width of the carrot garden, and the length of the strawberry garden was 8 metres longer than the length of the carrot garden. When Uncle Ferda fenced both gardens, he found that both had the same perimeter. Determine the dimensions of the carrot and strawberry gardens.

Final Answer:

a =  12 m
b =  12 m
c =  4 m
d =  20 m

Step-by-step explanation:

$$\begin{gathered} a=b \\ 4a=2\cdot (c+d) \\ c=a/3 \\ d=a+8 \\ 4a=2\cdot (c+d) \\ c=a/3 \\ d=a+8 \\ 4a=2\cdot (a/3+(a+8)) \\ 4\cdot a=2\cdot (a/3+(a+8)) \\ 4a=48 \\ a=\frac{48}{4}=12 \\ a=12=12\text{m} \end{gathered}$$

$b=a=12=12\text{m}$

$c=a/3=12/3=4\text{m}$

$d=a+8=12+8=20\text{m}$

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