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Chapter 1: Problem 7

The "scale" of a certain map is \(1 / 10000 .\) This means the length of, say, a road as represented on the map is \(1 / 10000\) the actual length of the road. What is the ratio of the area of a park as represented on the map to the actual area of the park? (tutorial: scaling)

Short Answer

Expert verified
Answer: The ratio of the area of a park as represented on the map to the actual area of the park is 1:100000000.

Step by step solution

01

Identify the scaling factor of length and width

In this case, the scaling factor for both length and width of the park between the map and the actual area is 1:10000.
02

Calculate the area scaling factor

To find the ratio of the areas, we need to square the scaling factor since we need to scale the length and width together (Area = Length * Width). If the scaling factor is 1:10000 for length and width, then for area, it would be \((1/10000)^2\).
03

Simplify the area scaling factor

Now, let's simplify the area scaling factor by squaring the ratio \((1/10000)^2\): \((1/10000)^2 = 1/100000000\)
04

Write the final ratio

The ratio of the area of a park as represented on the map to the actual area of the park is 1:100000000.

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