Suppose I use a scale on my map where every 3 inches on my map represents 5 miles. If a region on my map has an area of 45 square inches, what is the area of the actual region it represents?

hi I need help with this question, I don't know what to do.

thanks

5 mi/3 in

look at squares on map
5 miles * 5 miles = 3 in * 3 in
so
25 mi^2/9 in^2

45 in^2 * (25 mi^2/9 in^2) = 45*25/9 mi^2

= 125 mi^2

3 in = 5 mi

squaring ... 9 in^2 = 25 mi^2

a = (45/9) * 25 mi^2

but why are we using these numbers.. why are we multiplying or diving??

To find the area of the actual region represented on the map, you need to use the scale provided.

First, you need to determine how many inches on the map represent one mile. In this case, the scale tells us that every 3 inches on the map represents 5 miles. To find the ratio of inches to miles, you can write it as a fraction:

3 inches / 5 miles

Now, you want to find the area of the actual region, so you need to use this ratio to scale up the area.

Let's call the area of the actual region "A".

According to the scale, every 3 inches on the map represents 5 miles. So, 3 inches on the map represent an area of 5 miles x 5 miles = 25 square miles.

Therefore, the ratio of inches to square miles can be written as:

3 inches / 25 square miles

Now, you can set up a proportion:

3 inches / 25 square miles = 45 square inches / A square miles

To solve for A, you can cross multiply and divide:

3 inches x A square miles = 45 square inches x 25 square miles

3A = 1125

Divide both sides of the equation by 3 to solve for A:

A = 375

Therefore, the area of the actual region represented on the map is 375 square miles.