Question

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? inch to miles (lesson 1 - 12)

Explanation:

Step1: Find the ratio of the areas

Let the ratio of the areas of the scale - drawing to the actual area be $\frac{A_{scale}}{A_{actual}}$. Here, $A_{scale}=10$ square inches and $A_{actual} = 25000$ square miles. So, $\frac{A_{scale}}{A_{actual}}=\frac{10}{25000}=\frac{1}{2500}$.

Step2: Find the ratio of the lengths

For a scale - drawing, if the ratio of the areas is $k$, the ratio of the corresponding lengths (scale) is $\sqrt{k}$. Let the scale be $1:x$. Then, since the ratio of the areas is $\frac{1}{2500}$, the ratio of the lengths is $\sqrt{\frac{1}{2500}}=\frac{1}{50}$.

Answer:

1 inch to 50 miles