Question

1. look at the map, and answer the following question.

serge is making map of a small town that is 5.7 miles long and 4.3 miles wide. if he is using the scale 1 inch = 0.5 miles, how large will his map be?

22.8 x 17.2 inches
2.85 x 2.15 inches
11.4 x 8.6 inches
5.7 x 4.3 inches

Explanation:

Step1: Calculate map length

The scale is 1 inch = 0.5 miles. For the length of 5.7 miles, the map length is $5.7\div0.5 = 11.4$ inches? Wait, no, wait. Wait, no, wait, 1 inch is 0.5 miles, so to find inches from miles, we divide miles by 0.5 (since 0.5 miles per inch, so inches = miles / 0.5). Wait, no, 1 inch represents 0.5 miles, so the number of inches is miles divided by 0.5. Wait, 5.7 miles long: inches for length is $5.7\div0.5 = 11.4$? Wait, no, wait, 0.5 miles per inch, so 1 mile is 2 inches. So 5.7 miles is 5.7 * 2 = 11.4 inches? Wait, no, 1 inch = 0.5 miles, so to get inches, we do miles / 0.5. So 5.7 / 0.5 = 11.4 inches. Similarly, width is 4.3 miles, so 4.3 / 0.5 = 8.6 inches. Wait, but the options have 11.4 x 8.6? Wait, but let's check again. Wait, maybe I made a mistake. Wait, 1 inch = 0.5 miles, so the scale factor is 0.5 miles per inch. So the map distance (in inches) = actual distance (in miles) / scale (miles per inch). So length: 5.7 / 0.5 = 11.4 inches. Width: 4.3 / 0.5 = 8.6 inches. So the map size is 11.4 x 8.6 inches? Wait, but the options include that. Wait, but let's check the options again. The options are:

22.8 x 17.2, 2.85 x 2.15, 11.4 x 8.6, 5.7 x 4.3.

Wait, maybe I messed up. Wait, 1 inch = 0.5 miles, so to convert miles to inches, we multiply by (1 inch / 0.5 miles) = 2 inches per mile. So 5.7 miles 2 inches/mile = 11.4 inches. 4.3 miles 2 inches/mile = 8.6 inches. So the map is 11.4 x 8.6 inches. So the correct option is 11.4 x 8.6 inches. Wait, but let's check the options. Yes, that's one of the options.

Wait, but let's re-express the calculation.

Step1: Calculate map length

Actual length = 5.7 miles. Scale: 1 inch = 0.5 miles. So map length (L) = 5.7 / 0.5 = 11.4 inches.

Step2: Calculate map width

Actual width = 4.3 miles. Map width (W) = 4.3 / 0.5 = 8.6 inches.

So the map size is 11.4 x 8.6 inches.

Answer:

11.4 x 8.6 inches (the option corresponding to this, which is one of the choices, likely the third option: 11.4 x 8.6 inches)