Question

2) A map of a park has a scale of 1 inch to 1,000 feet. Another map of the same park has a scale of 1 inch to 500 feet which map is larger? Explain or show your reasoning.

Answer 1

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:

`\frac{1\text{ inch}}{x\text{ inches}}=\frac{500\text{ ft}}{1000\text{ ft}}`

Solving for x:

`\begin{gathered} 1\cdot1000=500\cdot x \\ (1000)/(500)=x \\ 2\text{ inches = x} \end{gathered}`

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.