Garden fencing cost

We want to enclose a rectangular garden whose length-to-width ratio is 2:1 and whose half of the perimeter borders the road. The fencing path along the road costs 7 euros per meter, and the other fencing costs only 3 euros per meter. How many acres does a garden have if its fencing costs 363 euros?

Final Answer:

a =  24.2 m
b =  12.1 m
S =  2.9282 a

Step-by-step explanation:

$$\begin{gathered} a=2b \\ 7\cdot (a+b)+3\cdot (a+b)=363 \\ 7\cdot (2b+b)+3\cdot (2b+b)=363 \\ 7\cdot (2\cdot b+b)+3\cdot (2\cdot b+b)=363 \\ 30b=363 \\ b=\frac{363}{30}=12.1 \\ b=\frac{121}{10}=12.1 \\ a=2\cdot b=2\cdot 12.1=24.2\text{m} \end{gathered}$$

$$\begin{gathered} S_1=a\cdot b=24.2\cdot 12.1=\frac{14641}{50}=292.82{\text{m}}^2 \\ S=S_1\to \text{a}=S_1:100\text{a}=292.82:100\text{a}=2.928\text{a}=2.9282\text{a} \end{gathered}$$

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