Question

On a map, the scale shown is 1 inch : 5 miles. If a park is 75 square miles, what is the area of the park on the map?

Answer 1

Given:

On a map, the scale shown is 1 inch : 5 miles.

Area of park = 75 square miles.

To find:

The area of the park on the map.

Solution:

Ratio of the areas of similar figures is equal to the ratio square of their corresponding sides.

$\dfrac{\text{Area of park on the map}}{\text{Actual area of the park}}=\dfrac{\text{Side of park in map}^2}{\text{Actual side of park}^2}$

Let A be the area of the park on the map.

$\dfrac{A}{75}=\dfrac{1^2}{5^2}$

$A=\dfrac{1}{25}\times 75$

$A=3$

Therefore, the area of the park on the map is 3 square inches.