Determining Lawn Quantity for Soccer Field

Let's determine the number of rectangular shaped lawns needed to cover the soccer field. First, we need to calculate the dimensions of the soccer field using the given perimeter. The perimeter \( P \) of a rectangle is given by: \[ P = 2 \times (\text{length} + \text{breadth}) \] Given \( P = 346 \, \text{m} \), we can set up the following equation: \[ 346 = 2 \times (\text{length} + \text{breadth}) \] \[ 173 = \text{length} + \text{breadth} \] Since we're not given specific values for length and breadth, let's denote: \[ \text{length} = L \] \[ \text{breadth} = B \] So, \[ L + B = 173 \] For simplicity, we can assume several practical dimensions for a soccer field, though an exact length and breadth will still fulfill \( L + B = 173 \). To find the total area, we can use: \[ \text{Area of soccer field} = L \times B \] Next, we need to calculate the area of one rectangular shaped lawn. Each lawn piece measures \( 10 \, \text{m} \times 5 \, \text{m} \), so: \[ \text{Area of one lawn piece} = 10 \times 5 = 50 \, \text{m}^2 \] Now, let's find how many such lawn pieces are needed to cover the entire soccer field. We need to divide the total area of the soccer field by the area of one lawn piece. Let’s consider general dimensions for \( L \) and \( B \). To make things simple, choose \( L = 100 \) and \( B = 73 \) (since 100 + 73 = 173). These dimensions are close to the ratio seen in actual soccer fields. So, the area of the soccer field is: \[ \text{Area of soccer field} = 100 \times 73 = 7300 \, \text{m}^2 \] Now, divide this area by the area of one lawn piece: \[ \text{Number of lawn pieces} = \frac{\text{Area of soccer field}}{\text{Area of one lawn piece}} = \frac{7300}{50} = 146 \] Thus, 146 rectangular shaped lawn pieces are required to cover the soccer field. The constructor claimed that more than 150 pieces are needed but based on the calculations, only 146 pieces are needed. So, the actual number of rectangular shaped lawns needed to cover the soccer field is: \[ \boxed{146} \]