Question

The scale of a certain map is 4/5 inch = 16 miles. A square park is represneted on the map by a square with side length 5/8 inch. What is the actual area of this park? Express your area as a decimal to the nearest hundredth.

Answer 1

Answer:

The area of this park is 130.60 square miles.

Step-by-step explanation:

Given : The scale of a certain map is $\frac{4}{5}$ inch = 16 miles. A square park is represented on the map by a square with side length $\frac{5}{8}$ inch.

To find : What is the actual area of this park?

Solution :

The scale of a certain map is $\frac{4}{5}$ inch = 16 miles.

Let the side length of $\frac{5}{8}$ inch = x miles.

So, $\dfrac{\frac{4}{5}}{\frac{5}{8}}=\dfrac{16}{x}$

$\dfrac{4\times 8}{5\times5}=\dfrac{16}{x}$

$\dfrac{32}{25}=\dfrac{16}{x}$

$x=\dfrac{16\times 25}{35}$

$x=11.428$

The side length of a square is 11.428 miles.

The area of the square is $A=s^2$.

$A=(11.42)^2$

$A=130.599\ miles^2$

To nearest hundredth,

The area of this park is 130.60 square miles.