A structural engineer is analyzing a blueprint for a steel bridge truss. The blueprint use… — Armed Services Vocational Aptitude Battery (ASVAB)

A structural engineer is analyzing a blueprint for a steel bridge truss. The blueprint uses a scale where $\frac{7}{8}\text{ inch}$ represents an actual length of $21\text{ feet}$ . If a particular support beam measures $6.5\text{ inches}$ on the blueprint, what is the actual length of this beam in feet?

Answer: 156 feet

Answer

156

The correct answer is found by establishing a proportion based on the scale. Since

\frac{7}{8}\text{ inch}

equals

21\text{ feet}

1\text{ inch}

must equal

21 \div \frac{7}{8}

, which is

24\text{ feet}

. Multiplying the blueprint length of

6.5\text{ inches}

by this unit rate of

24

gives an actual length of

156\text{ feet}

Step-by-Step Solution

Determine the unit scale factor in feet per inch.

21 \div \frac{7}{8} = 24\text{ feet/inch}

Finding the actual distance represented by a single inch creates a simple multiplier for any dimension on the blueprint.

Multiply the measurement on the blueprint by the unit scale factor.

6.5 \times 24 = 156\text{ feet}

Scaling up the drawing measurement by the unit rate yields the actual real-world length of the beam.

Key Concept

Direct proportions and unit rates in scale drawings

Alternative Method

You can set up a direct proportion:

\frac{\frac{7}{8}}{21} = \frac{6.5}{x}

. Cross-multiplying gives

\frac{7}{8}x = 136.5

. Multiplying both sides by

\frac{8}{7}

yields

x = 156

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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