Calculate the actual length of the property line based on the given scale and enter the ex… — Armed Services Vocational Aptitude Battery (ASVAB)

Calculate the actual length of the property line based on the given scale and enter the exact numerical value.

Answer:A city surveyor is examining a property deed map that uses a scale of

1\frac{1}{2}\text{ inches} = 40\text{ feet}

. If the eastern boundary line measures

5\frac{1}{4}\text{ inches}

on this map, the actual length of the boundary line is 【140】 feet.

140

The correct answer is found by setting up a direct proportion based on the scale:

\frac{1.5\text{ inches}}{40\text{ feet}} = \frac{5.25\text{ inches}}{x\text{ feet}}

. Cross-multiplying gives

1.5x = 210

, and dividing by

1.5

gives an actual length of

140

feet.

Convert the mixed fractions into decimals for easier algebraic calculation.

The map scale is

1.5\text{ inches} = 40\text{ feet}

. The measured boundary is

5.25\text{ inches}

Working with decimals simplifies the process of setting up and solving a proportion.

Set up a direct proportion comparing the map distance to the actual distance.

\frac{1.5\text{ inches}}{40\text{ feet}} = \frac{5.25\text{ inches}}{x\text{ feet}}

A map's scale establishes a consistent ratio between the dimensions on the drawing and the true physical dimensions.

Cross-multiply the terms to isolate the unknown variable

x

1.5x = 40 \times 5.25

Cross-multiplication transforms the proportion into a linear equation that is easy to solve.

Multiply the values on the right side of the equation.

40 \times 5.25 = 210

Simplifying the right side to

210

leaves a basic one-step algebraic equation:

1.5x = 210

Divide both sides by

1.5

to solve for

x

x = \frac{210}{1.5} = 140

Dividing by the coefficient isolates

x

, revealing the actual length of the boundary line in feet.

Using proportional reasoning and cross-multiplication to convert map measurements to real-world distances.

Question