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Difficulty: Very hardScale Drawings and Map Measurements

A landscape architect is reviewing a scale drawing of a rectangular park. On the drawing, the scale is indicated as 23\frac{2}{3} inch = 1212 yards. The perimeter of the park on the drawing is 1414 inches, and its length is 4124\frac{1}{2} inches. What is the actual width of the park in feet?

  1. A
    15
  2. B
    45
  3. C
    60
  4. 135Answer

Answer

135
To find the correct answer, three phases are required. First, use the perimeter formula (P=2L+2WP = 2L + 2W) to find the drawing width: 14=2(4.5)+2W→W=2.514 = 2(4.5) + 2W \rightarrow W = 2.5 inches. Next, find the unit scale by dividing 1212 yards by 23\frac{2}{3} inch, yielding 1818 yards per inch. Multiplying the 2.52.5-inch drawing width by 1818 gives an actual width of 4545 yards. Finally, convert yards to feet by multiplying by 33, resulting in 135135 feet.

Step-by-Step Solution

1
Determine the width of the park on the scale drawing.
The width on the drawing is 2.52.5 inches.
The formula for the perimeter of a rectangle is P=2L+2WP = 2L + 2W. Substituting the given values, 14=2(412)+2W14 = 2(4\frac{1}{2}) + 2W, which simplifies to 14=9+2W14 = 9 + 2W. Solving for WW gives 2W=52W = 5, so W=2.5W = 2.5.
2
Calculate the unit scale rate.
11 inch on the drawing represents 1818 yards in reality.
To find the value of 11 inch, divide the actual distance by the drawing distance: 12÷23=12×32=1812 \div \frac{2}{3} = 12 \times \frac{3}{2} = 18 yards per inch.
3
Calculate the actual width of the park in yards.
The actual width is 4545 yards.
Multiply the drawing width by the unit scale rate: $2.5 \text{ inches} \times 18 \text{ yards/inch} = 45 \text{ yards}.
4
Convert the actual width from yards to feet.
The final actual width is 135135 feet.
There are 33 feet in 11 yard. Multiply the width in yards by 33: 45×3=13545 \times 3 = 135 feet.

Key Concept

Combining geometric perimeter calculations with multi-step scale and unit conversions.
Estimated Time:3m 0s
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Topics

Scale Drawings and Map Measurements

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