An architect is designing a community center and reviewing the floor plan. The floor plan … — Armed Services Vocational Aptitude Battery (ASVAB)

An architect is designing a community center and reviewing the floor plan. The floor plan uses a scale of $\frac{3}{4}\text{ inch} = 5\text{ feet}$ . If the main hall measures $4.5\text{ inches}$ long on the floor plan, what is the actual length of the main hall in feet?

Answer: 30 feet

Answer

The correct answer is found by setting up a proportion or finding the unit rate. Since

\frac{3}{4}\text{ inch}

represents

5\text{ feet}

1\text{ inch}

represents

\frac{20}{3}\text{ feet}

. Multiplying the drawing measurement of

4.5\text{ inches}

\frac{20}{3}\text{ feet per inch}

yields exactly

30\text{ feet}

Step-by-Step Solution

Find the actual distance represented by one inch.

1\text{ inch} = 5 \div \frac{3}{4} = 5 \times \frac{4}{3} = \frac{20}{3}\text{ feet}

Establishing a unit rate simplifies calculating the actual length for any given map measurement.

Multiply the unit rate by the blueprint measurement.

4.5 \times \frac{20}{3} = \frac{9}{2} \times \frac{20}{3} = \frac{180}{6} = 30\text{ feet}

Multiplying the map length by the actual distance per inch gives the total actual length.

Key Concept

Solving scale drawing problems using proportions or unit rates.

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