Calculating Rectangles Needed to Cover a Soccer Field

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.] ```