On a map the scale showing is 1 inch by 5 mi if a park is 75 square miles what is the area of the park on the map. The parks area is _ square inches on the map
The Correct Answer and Explanation is:
To find the area of the park on the map, we need to first understand the relationship between the scale on the map and the actual area of the park in real life.
Step 1: Understanding the scale
The scale given is “1 inch = 5 miles.” This means that for every 1 inch on the map, the corresponding real-world distance is 5 miles.
Step 2: Calculate the side length of the park
Since the area of the park is given as 75 square miles, we can calculate the side length of the park in miles, assuming the park is roughly square-shaped. To do this, we take the square root of 75, because area is the square of the side length:
[
\text{Side length of the park} = \sqrt{75} \approx 8.66 \text{ miles}
]
Step 3: Convert the side length to the map scale
Now, using the map scale of 1 inch = 5 miles, we need to convert the side length of the park in miles (8.66 miles) into inches on the map. Since 1 inch represents 5 miles, we divide the side length of the park by 5:
[
\text{Side length on the map} = \frac{8.66 \text{ miles}}{5} \approx 1.73 \text{ inches}
]
Step 4: Calculate the area on the map
Now that we know the side length of the park on the map is approximately 1.73 inches, we can calculate the area on the map by squaring this value:
[
\text{Area on the map} = (1.73 \text{ inches})^2 \approx 2.99 \text{ square inches}
]
Final Answer:
The area of the park on the map is approximately 3 square inches.
Explanation:
The map uses a scale of 1 inch = 5 miles, meaning each inch on the map represents a 5-mile distance in real life. To find the area of the park on the map, we first calculated the side length of the park, which we assumed to be a square, and converted that into map inches by using the scale. Finally, we squared the side length to determine the area on the map. The result is approximately 3 square inches. This process involves understanding the scale conversion and applying it to both the length and area measurements.