Determining Rectangular Lawns Needed for Soccer Field Coverage

To determine how many 10 m by 5 m rectangular pieces of lawn are needed to cover a soccer field, we need to know the total area of the soccer field. Since the constructor claims that they need more than 150 rectangular shapes, let's first calculate the total area covered by 150 rectangles. 1. Calculate the area of one rectangle: \[ \text{Area of one rectangle} = \text{length} \times \text{breadth} = 10 \, \text{m} \times 5 \, \text{m} = 50 \, \text{m}^2 \] 2. Calculate the total area covered by 150 rectangles: \[ \text{Total area for 150 rectangles} = 150 \times 50 \, \text{m}^2 = 7500 \, \text{m}^2 \] Since it is claimed that more than 150 rectangles are needed, the area of the soccer field must be more than 7500 m². However, without knowing the precise dimensions of the soccer field, we can't determine the exact number of rectangles needed beyond just assuming it's more than 150. To find the exact number of rectangles needed, let's solve this step-by-step: 1. Assume the area of the soccer field is \(A\). 2. Find the minimum number of rectangles needed by dividing the total area of the soccer field by the area of one rectangle, and then round up to the nearest whole number. 3. Let the number of rectangles be \(N\). So the calculation becomes: \[ N = \left\lceil \frac{A}{50} \right\rceil \] Where \(\left\lceil x \right\rceil\) denotes the ceiling function (rounding up to the nearest integer). If \(A > 7500 \, \text{m}^2\), then we can infer that: \[ N > \frac{7500}{50} = 150 \] Therefore, \(N\) must be more than 150 rectangles. Without the exact area \(A\), we can only say that if \(A \approx 7600 \, \text{m}^2\), then: \[ \frac{7600}{50} = 152 \] So, the constructor may indeed need more than 150 rectangles, likely around 152 or more, depending on the exact total area of the soccer field.