A civil engineer creates a scale drawing of a rectangular park using a scale where 2.5\tex… — GRE General Test

A civil engineer creates a scale drawing of a rectangular park using a scale where $2.5\text{ inches}$ on the drawing represents an actual distance of $12\text{ feet}$ . On this initial blueprint, the park has a length of $15\text{ inches}$ and a width of $10\text{ inches}$ . If the engineer creates a second blueprint of the same park using a scale where $3\text{ inches}$ represents an actual distance of $16\text{ feet}$ , what is the perimeter, in inches, of the park on the second blueprint?

A
$22.5\text{ inches}$
B
$37.5\text{ inches}$
C
$40.5\text{ inches}$
$45\text{ inches}$ Answer
E
$60\text{ inches}$

Answer

45 inches

The correct answer is

45\text{ inches}

. The perimeter on the first blueprint is

2 \times (15 + 10) = 50\text{ inches}

. Since

2.5\text{ inches}

represents

12\text{ feet}

, each inch on the first drawing represents

\frac{12}{2.5} = 4.8\text{ feet}

. Thus, the actual perimeter of the park is

50 \times 4.8 = 240\text{ feet}

. On the second blueprint,

16\text{ feet}

is represented by

3\text{ inches}

, meaning

1\text{ foot}

is represented by

\frac{3}{16}\text{ inches}

. Therefore, the perimeter on the second drawing is

240 \times \frac{3}{16} = 45\text{ inches}

Step-by-Step Solution

Calculate the perimeter of the park on the first blueprint.

Perimeter on first blueprint =

2 \times (15 + 10) = 50\text{ inches}

The perimeter of a rectangle is calculated as

2 \times (\text{length} + \text{width})

Determine the actual perimeter of the park in feet using the first scale (

2.5\text{ inches} = 12\text{ feet}

Actual perimeter =

50\text{ inches} \times \left(\frac{12\text{ feet}}{2.5\text{ inches}}\right) = 240\text{ feet}

Multiplying by the ratio of actual feet per blueprint inch gives the true physical perimeter.

Convert the actual perimeter to inches on the second blueprint using the second scale (

3\text{ inches} = 16\text{ feet}

Perimeter on second blueprint =

240\text{ feet} \times \left(\frac{3\text{ inches}}{16\text{ feet}}\right) = 45\text{ inches}

Multiplying the actual distance in feet by the second blueprint scale ratio yields the required blueprint perimeter.

Key Concept

Scale ratios and linear proportional conversions

Estimated Time:1m 30s

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