To determine how much fencing will be needed for Kai's garden, we need to find the perimeter of the garden, which is the total length of all four sides.
Let's denote the area of the garden as \( A \) and the formula for the area of a rectangle as:
\[ A = \text{length} \times \text{width} \]
Kai remembers that the area is 121 ft². The perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]
To proceed, we can explore possible values for length and width. If we assume \( \text{length} = l \) and \( \text{width} = w \), we know:
\[ l \times w = 121 \]
There are many factor pairs of 121, but for simplicity, let's consider the factor pairs:
- \( l = 1 \), \( w = 121 \)
- \( l = 11 \), \( w = 11 \)
- \( l = 121 \), \( w = 1 \)
Calculating the perimeter for these pairs:
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For \( l = 1 \), \( w = 121 \): \[ P = 2(1 + 121) = 2 \times 122 = 244 \text{ feet} \]
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For \( l = 11 \), \( w = 11 \) (this is a square): \[ P = 2(11 + 11) = 2 \times 22 = 44 \text{ feet} \]
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For \( l = 121 \), \( w = 1 \): \[ P = 2(121 + 1) = 2 \times 122 = 244 \text{ feet} \]
Since there are multiple possible configurations for length and width, the perimeter (amount of fencing needed) can vary depending on the dimensions chosen.
However, if we assume that Kai's garden is square (the most efficient shape for a given area), then the best dimensions would be:
\[ \text{length} = \text{width} = \sqrt{121} = 11 \text{ ft} \] Thus:
\[ \text{Total length of fencing needed} = P = 2(11 + 11) = 44 \text{ feet} \]
Therefore, Kai will need 44 feet of fencing for his garden.