On a map of Ohio, the cities of Dayton, Columbus, and Cincinnati form a triangle whose sides are shown in the figure below. The actual distance from Dayton to Cincinnati is 48 miles. What is the actual distance between Cincinnati and Columbus?

The actual distance between Cincinnati and Columbus is 106 miles

Step-by-step explanation: The diagram in the question shows three cities at each point of the triangle and the distances are expressed in inches. In actual fact the real distance between one city and another is measured in miles. This means what we have in the diagram is simply a distance scaled down to a smaller unit. Simply put, we have to find the scale factor to determine the “Actual” distance.

However, we already have a clue. The distance between Dayton and Cincinnati is 48 miles, but has been scaled down by a factor which can be determined by

Scale factor = Actual Distance/scale measurement

Scale factor = 48/2.4

Scale factor = 20

What this means is that the scale measurement multiplied by 20 gives us the actual distance (and the actual distance divided by the scale measurement gives us the scale factor).

Therefore to calculate the distance between Cincinnati and Columbus,

Scale measurement x 20 = actual distance

5.3 x 20 = actual distance

106 = actual distance

The distance between Cincinnati and Columbus is 106 miles.

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