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# Determining Lawn Pieces Required for Soccer Field Coverage

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Question: The perimeter of soccer field is 346m L : 105 B: 68 The lawn needed to cover the soccer field is solid in 10 m by 5 m rectangles The constructor claims that they need more than 150 rectangular shaped lawn to cover the soccer field, determine the number of rectangular shaped lawn needed. You may use the formula: Area of a rectangle= length× breadth

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To determine the number of rectangular shaped lawns needed to cover the soccer field, we need to use the given dimensions and the formula for the area of a rectangle. First, let's calculate the area of the soccer field: $\text{Area of soccer field} = \text{Length} \times \text{Breadth} = 105 \, \text{m} \times 68 \, \text{m} = 7140 \, \text{m}^2$ Next, let's calculate the area of one rectangular-shaped lawn piece: $\text{Area of one lawn piece} = \text{Length} \times \text{Breadth} = 10 \, \text{m} \times 5 \, \text{m} = 50 \, \text{m}^2$ Now, we need to determine how many such pieces are required to cover the total area of the soccer field: $\text{Number of lawn pieces needed} = \frac{\text{Area of soccer field}}{\text{Area of one lawn piece}} = \frac{7140 \, \text{m}^2}{50 \, \text{m}^2} = 142.8$ Since we can’t have a fraction of a lawn piece, we must round up to the next whole number to ensure the entire area is covered. Therefore, we need: $\lceil 142.8 \rceil = 143 \text{ lawn pieces}$ The constructor claims that more than 150 lawn pieces are needed, but based on our calculations, only 143 pieces are actually required. Therefore, the constructor's claim is incorrect.

Aug. 12, 2024, 8:01 a.m.

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