Let's suppose the park is 1,000 ft long. In the case we use the scale of 1 inch to 1,000 feet the scaled map would be 1 inch long.
To find the length of the scaled map that uses the scale of 1 inch to 500 feet we can apply the next proportion:
[tex]\frac{1\text{ inch}}{x\text{ inches}}=\frac{500\text{ ft}}{1000\text{ ft}}[/tex]Solving for x:
[tex]\begin{gathered} 1\cdot1000=500\cdot x \\ \frac{1000}{500}=x \\ 2\text{ inches = x} \end{gathered}[/tex]Therefore, the length would be 2 inches, which is greater than the first case. No matter what is the length, or the dimensions in general, of the park, the scaled map that uses the scale of 1 inch to 500 feet will be always larger.
