Question

from unit 1, lesson 12
the area of the mojave desert is 25,000 square miles. a scale drawing of the mojave desert has an area of 10 square inches. what is the scale of the map?

Explanation:

Step1: Find the ratio of areas

The ratio of the area on the scale - drawing to the actual area is \(\frac{10}{25000}=\frac{1}{2500}\).

Step2: Find the ratio of lengths

If the ratio of areas of two similar figures (the scale - drawing and the actual desert) is \(A_1:A_2\), and the ratio of their corresponding side - lengths is \(l_1:l_2\), then \(A_1:A_2=(l_1:l_2)^2\). Let the ratio of lengths (scale) be \(x:y\). We know that \((x:y)^2=\frac{1}{2500}\). Taking the square root of both sides, \(x:y = \sqrt{\frac{1}{2500}}\).

Since \(\sqrt{\frac{1}{2500}}=\frac{1}{50}\), the scale of the map is \(1\) inch represents \(50\) miles.

Answer:

The scale of the map is \(1\) inch represents \(50\) miles.