Answer :
Answer:
The area of this park is 130.60 square miles.
Step-by-step explanation:
Given : The scale of a certain map is [tex]\frac{4}{5}[/tex] inch = 16 miles. A square park is represented on the map by a square with side length [tex]\frac{5}{8}[/tex] inch.
To find : What is the actual area of this park?
Solution :
The scale of a certain map is [tex]\frac{4}{5}[/tex] inch = 16 miles.
Let the side length of [tex]\frac{5}{8}[/tex] inch = x miles.
So, [tex]\dfrac{\frac{4}{5}}{\frac{5}{8}}=\dfrac{16}{x}[/tex]
[tex]\dfrac{4\times 8}{5\times5}=\dfrac{16}{x}[/tex]
[tex]\dfrac{32}{25}=\dfrac{16}{x}[/tex]
[tex]x=\dfrac{16\times 25}{35}[/tex]
[tex]x=11.428[/tex]
The side length of a square is 11.428 miles.
The area of the square is [tex]A=s^2[/tex].
[tex]A=(11.42)^2[/tex]
[tex]A=130.599\ miles^2[/tex]
To nearest hundredth,
The area of this park is 130.60 square miles.