To find the missing side length or the actual distances using a map scale, set up a proportion with the given scale and solve for the unknown value by cross-multiplying. For example, using a scale of 1 inch = 5.5 miles, 16.5 miles is equivalent to 3 inches on a map, and with a scale of 0.5 inch = 100 miles, 8.1 inches translates to 1620 miles.
The correct answer to the given question is option c).
To solve the problems related to scale measurements and actual distances, we need to set up proportions and solve for the unknown value. Let's address this step-by-step for a couple of examples from the provided question set.
Using the scale 1 inch = 5.5 miles:
Example 1: To find the scale length that represents 16.5 miles, we set up a proportion using the scale:
scale/actual = 1 inch / 5.5 miles
1/5.5 = x/16.5
To find the value of x, we cross-multiply and solve:
5.5x = 16.5
x = 16.5 / 5.5
x = 3 inches
So, 16.5 miles would be represented by 3 inches on the map.
Using the scale 0.5 inch = 100 miles:
Example 2: To determine the number of actual miles for 8.1 inches on the map, we again set up a proportion:
0.5 inch/100 miles = 8.1 inches/x miles
0.5/100 = 8.1/x
Again, we cross-multiply and solve for x:
0.5x = 810
x = 810 / 0.5
x = 1620 miles
Therefore, 8.1 inches on the map equates to 1620 actual miles.
The probable question may be:
Find the missing side length. Round to the nearest tenth if necessary.
a) 6.3 mi
b) 9.0 mi
c) 16.5 mi
d) 18.7 mi