Questions: A map has a scale of 1''=50, how long is a property line on the map if the distance in the field measured to be 532.5'? 11.65 inches 10.56 inches 10.65 feet 10.65 inches

A map has a scale of 1''=50, how long is a property line on the map if the distance in the field measured to be 532.5'?
11.65 inches
10.56 inches
10.65 feet
10.65 inches

Transcript text: A map has a scale of $1^{\prime \prime}=50$, how long is a property line on the map if the distance in the field measured to be 532.5'? 11.65 inches 10.56 inches 10.65 feet 10.65 inches

Solution

Solution Steps

To solve the problem, we need to convert the real-world distance to the map distance using the given scale. The scale is $1^{\prime \prime} = 50'$, which means 1 inch on the map represents 50 feet in the real world. We will divide the real-world distance by the scale factor to find the map distance in inches.

Solution Approach

Identify the real-world distance (532.5 feet).
Identify the scale (1 inch = 50 feet).
Divide the real-world distance by the scale factor to get the map distance in inches.

Step 1: Identify the Given Values

We are given the real-world distance of the property line as $ 532.5 $ feet and the scale of the map as $ 1^{\prime \prime} = 50 $ feet.

Step 2: Set Up the Calculation

To find the length of the property line on the map in inches, we use the formula: \[ \text{Map Distance (inches)} = \frac{\text{Real World Distance (feet)}}{\text{Scale Factor (feet per inch)}} \] Substituting the known values: \[ \text{Map Distance} = \frac{532.5 \text{ feet}}{50 \text{ feet/inch}} \]

Step 3: Perform the Calculation

Calculating the above expression: \[ \text{Map Distance} = 10.65 \text{ inches} \]