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A scale on a map of a national park reads 1 inch equals 0.25 miles. The national park is roughly in the shape of a rectangle. If the map of the park is 12 inches tall and 8 inches wide, estimate the total area of the park.

A. [tex][tex]$96 \text{ mi}^2$[/tex][/tex]
B. [tex][tex]$6 \text{ mi}^2$[/tex][/tex]
C. [tex][tex]$24 \text{ mi}^2$[/tex][/tex]
D. [tex][tex]$5 \text{ mi}^2$[/tex][/tex]

Sagot :

GinnyAnswer
To find the total area of the national park, we'll follow these steps:

1. Determine the conversion factor: The scale given is 1 inch = 0.25 miles. This means for every inch on the map, it represents 0.25 miles in real life.

2. Convert the dimensions of the park from inches to miles:
- The map is 12 inches tall. Therefore, the real-life height of the park is:
[tex]\[ 12 \text{ inches} \times 0.25 \text{ miles/inch} = 3 \text{ miles} \][/tex]
- The map is 8 inches wide. Therefore, the real-life width of the park is:
[tex]\[ 8 \text{ inches} \times 0.25 \text{ miles/inch} = 2 \text{ miles} \][/tex]

3. Calculate the area of the park: The area [tex]\(A\)[/tex] of a rectangle is given by the formula:
[tex]\[ A = \text{height} \times \text{width} \][/tex]
Using the converted dimensions:
[tex]\[ A = 3 \text{ miles} \times 2 \text{ miles} = 6 \text{ square miles} \][/tex]

Therefore, the total area of the national park is:
[tex]\[ 6 \text{ square miles} \][/tex]

The correct answer is [tex]\(6 \text{ mi}^2\)[/tex].
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