To determine how much fencing Kai needs for all four sides of his garden, we first need to understand the dimensions of the garden given that the area is 121 square feet (ft²).
If we assume the garden is rectangular, we can denote the length by \( l \) and the width by \( w \). The area of a rectangle is given by the formula:
\[ \text{Area} = l \times w \]
Given that the area is 121 ft², we have:
\[ l \times w = 121 \]
To find the perimeter of the garden, we can use the formula for the perimeter \( P \) of a rectangle:
\[ P = 2l + 2w = 2(l + w) \]
To find \( l + w \), we need some pairs of \( (l, w) \) that multiply together to equal 121. The pairs of factors of 121 are \( (1, 121) \) and \( (11, 11) \).
Let's calculate the perimeter for each pair of factors:
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For \( (l, w) = (1, 121) \): \[ l + w = 1 + 121 = 122 \] \[ P = 2(l + w) = 2 \times 122 = 244 \text{ ft} \]
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For \( (l, w) = (11, 11) \) (which is a square): \[ l + w = 11 + 11 = 22 \] \[ P = 2(l + w) = 2 \times 22 = 44 \text{ ft} \]
Thus, the amount of fencing needed will depend on how Kai's garden is shaped:
- If the garden is shaped as a \( 1 \) ft by \( 121 \) ft rectangle, he needs 244 ft of fencing.
- If the garden is a \( 11 \) ft by \( 11 \) ft square, he needs 44 ft of fencing.
Without additional information, either value could be correct based on the dimensions of the garden.