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# Calculating Rectangles Needed to Cover a Soccer Field

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Question: The perimeter of soccer field is 346m 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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Sure, let's break down the problem and determine the number of rectangular shaped lawns needed to cover the soccer field. First, understand that we are given: - The perimeter of the soccer field: $$P = 346$$ meters The formula for the perimeter $$P$$ of a rectangle is: $P = 2 \times (L + W)$ where $$L$$ is the length and $$W$$ is the width. Rewriting this formula to solve for the area: $346 = 2 \times (L + W)$ $173 = L + W$ To cover the soccer field with rectangular pieces, we need to know the area $$A$$ of the soccer field: $A = L \times W$ Since we don't know $$L$$ and $$W$$, find their values such that their sum is 173 meters (assuming the length $$L$$ is greater than or equal to the width $$W$$). Next, given the rectangular pieces of lawn are $$10$$ meters by $$5$$ meters, the area of each rectangular piece is: $\text{Area of each piece} = 10 \times 5 = 50 \text{ square meters}$ We need to cover the entire area of the soccer field with these pieces. Let's find out if 150 pieces are enough: $\text{Total area covered by 150 pieces} = 150 \times 50 = 7500 \text{ square meters}$ To determine whether we need more pieces, we need to approximate the area of the soccer field. Let's estimate: Suppose typical soccer field dimensions are used: Common dimensions range from: - Length: $$100$$ to $$110$$ meters - Width: $$64$$ to $$75$$ meters If we assume dimensions such as: Length (L) = $$110$$ meters Width (W) = $$63$$ meters These dimensions fit our perimeter (since $$L + W = 173$$): $2 \times (110 + 63) = 2 \times 173 = 346 \text{ meters}$ Now calculate the area with these approximations: $A = 110 \times 63 = 6930 \text{ square meters}$ Therefore, we find out whether 150 pieces would be sufficient: \[ 150 \) \ (\times\ 50\ )\ =\ 7500)\ \text{square meters} Since the area of the soccer field \approx 6930 square meters, 150 rectangular pieces of turf sufficient: Thus, the constructor's claim that he needs more than 150 rectangular pieces seems not accurate. c Calculation: Solid Solution needed approx 6930/50=139 rectangular pieces needed.] 

Aug. 12, 2024, 7:55 a.m.

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