An architectural blueprint for a new warehouse uses a scale where \frac{1}{4} \text{ inch}… — Armed Services Vocational Aptitude Battery (ASVAB)

An architectural blueprint for a new warehouse uses a scale where $\frac{1}{4} \text{ inch} = 3 \text{ feet}$ . If a storage room has an area of $5 \text{ square inches}$ on the blueprint, what is the actual area of the storage room in square feet?

A
15
B
45
C
60
720Answer

Answer

720

To find the actual area from a scale drawing, you must first convert the given scale to a unit linear scale. Multiplying

\frac{1}{4} \text{ inch} = 3 \text{ feet}

4

shows that

1 \text{ inch} = 12 \text{ feet}

. Because we are dealing with area (a 2D measurement), we must square this linear relationship:

1 \text{ square inch} = 12^2 \text{ square feet} = 144 \text{ square feet}

. Finally, multiplying the drawing's area of

5 \text{ square inches}

144 \text{ square feet per square inch}

yields

720 \text{ square feet}

Step-by-Step Solution

Find the linear scale rate for a full inch.

Since

\frac{1}{4} \text{ inch} = 3 \text{ feet}

, multiply both sides by

4

to get

1 \text{ inch} = 12 \text{ feet}

Establishing a base unit rate of

1 \text{ inch}

makes area calculations straightforward.

Convert the linear scale into an area scale factor.

Square both sides of the linear scale:

(1 \text{ inch})^2 = (12 \text{ feet})^2

, which simplifies to

1 \text{ square inch} = 144 \text{ square feet}

Area is a two-dimensional measurement, so the one-dimensional (linear) scale factor must be squared.

Calculate the actual area of the storage room.

Multiply the blueprint area by the area scale factor:

5 \times 144 = 720 \text{ square feet}

This scales the drawing's area up to the actual physical area.

Key Concept

When using scale drawings, the scale factor for area is the square of the linear scale factor.

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