To find the average number of people per square mile, we first need to determine the area of the county in square miles.
The area \( A \) of a rectangle can be calculated using the formula:
\[ A = \text{length} \times \text{width} \]
In this case, the length is 40 miles, and the width is 30 miles:
\[ A = 40 , \text{miles} \times 30 , \text{miles} = 1200 , \text{square miles} \]
Next, we can find the average population density (people per square mile) by dividing the total population by the total area:
\[ \text{Population Density} = \frac{\text{Total Population}}{\text{Area}} = \frac{50000}{1200} \]
Calculating this gives:
\[ \text{Population Density} \approx 41.67 \]
Rounding this to the nearest whole number gives us:
\[ 42 \]
Thus, the average number of people living in each square mile of the county is 42.
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