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Answer:
To determine the total length of the fence surrounding the two gardens, we first need to calculate the side length of the big square garden.
Given:
- Side length of the small square garden = 17 m
- Side length of the big square garden = 3 times the side length of the small garden
1. Side length of the big square garden:
\text{Side length of big garden} = 3 \times \text{Side length of small garden}
\text{Side length of big garden} = 3 \times 17
\text{Side length of big garden} = 51 \text{ m}
2. Calculating the total length of the fence:
The total length of the fence is the sum of the perimeters of the small and big gardens.
For a square garden, the perimeter is given by 4 \times \text{side length}.
The total length of the fence is:
\text{Total fence length} = 4 \times \text{Side length of small garden} + 4 \times \text{Side length of big garden}
\text{Total fence length} = 4 \times 17 + 4 \times 51
\text{Total fence length} = 68 + 204
\text{Total fence length} = 272 \text{ m}
Therefore, the total length of the fence surrounding the two gardens is 272 meters.
Step-by-step explanation:
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