Question

« the area of the Mojave desert is 25,000 square miles. A scale drawing has an area of 10 square inches. What is the scale of the map? »
I think the answer is 10 inches to 25,000 miles but I’m not sure.

Answer 1

The scale of the map will be:  1 inch = 50 miles

Explanation

Actual area of the Mojave desert is 25,000 square miles and the scale drawing has an area of 10 square inches.

Suppose, the scale of the map is:  1 inch = $x$ miles.

So, 1 square inches = $x^2$ square miles

and 10 square inches = $10x^2$ square miles

So, the equation will be .....

$10x^2 = 25000\\ \\ x^2 = \frac{25000}{10}=2500\\ \\ x= \sqrt{2500}=50$

Thus, the scale of the map will be:  1 inch = 50 miles.

Answer 2

Answer:

1 inch equals 50 miles.

Step-by-step explanation:

We have been given that area of he Mojave desert is 25,000 square miles. A scale drawing has an area of 10 square inches. We are asked to find the scale of the map.

First of all, we will take square roots of both areas to find the lengths of sides as:

$\sqrt{25,000}=\sqrt{2500\times 10}=\sqrt{50^2\times 10}=50\sqrt{10}$

$\sqrt{10}$

Upon comparing sides, we will get:

$50\sqrt{10}:\sqrt{10}=50:1$

Therefore, the scale of the map is 1 inch equals 50 miles.