A structural blueprint for a new commercial warehouse uses a scale of \frac{1}{2}\text{ in… — Armed Services Vocational Aptitude Battery (ASVAB)

A structural blueprint for a new commercial warehouse uses a scale of $\frac{1}{2}\text{ inch} = 15\text{ feet}$ . On the blueprint, the rectangular main storage floor measures $3\frac{1}{3}\text{ inches}$ in length and $2\frac{1}{5}\text{ inches}$ in width. What is the actual area of the main storage floor in square feet?

Answer: 6600 square feet

Answer

The actual area of the main storage floor is 6600 square feet.

To find the actual area, we first establish the true scale of the blueprint. Since

\frac{1}{2}\text{ inch}

represents

15\text{ feet}

1\text{ inch}

represents

30\text{ feet}

. The blueprint dimensions are given as mixed fractions:

3\frac{1}{3}\text{ inches}

and

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

. We convert these to the improper fractions

\frac{10}{3}

and

\frac{11}{5}

, and multiply each by the scale factor of

30

to find the actual dimensions. The actual length is

\frac{10}{3} \times 30 = 100\text{ feet}

, and the actual width is

\frac{11}{5} \times 30 = 66\text{ feet}

. Finally, the area of the rectangle is found by multiplying the actual length by the actual width, yielding

100 \times 66 = 6600\text{ square feet}

Step-by-Step Solution

Determine the unit scale rate.

1\text{ inch} = 30\text{ feet}

The scale is given as

\frac{1}{2}\text{ inch} = 15\text{ feet}

. Multiplying both sides by

2

provides the actual distance per single inch on the drawing.

Calculate the actual length of the storage floor.

100\text{ feet}

Convert

3\frac{1}{3}

to the improper fraction

\frac{10}{3}

, then multiply by the scale factor of

30

\frac{10}{3} \times 30 = 100

Calculate the actual width of the storage floor.

66\text{ feet}

Convert

2\frac{1}{5}

to the improper fraction

\frac{11}{5}

, then multiply by the scale factor of

30

\frac{11}{5} \times 30 = 66

Calculate the actual area of the rectangular floor.

6600\text{ square feet}

Area is found by multiplying the actual length by the actual width:

100 \times 66 = 6600

Key Concept

Scale Drawings and Map Measurements

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