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Difficulty: MediumScale Drawings

A landscape architect is preparing a design layout for a new rectangular community garden. On the layout, the garden measures 2.5 inches2.5\text{ inches} in width and 5 inches5\text{ inches} in length. The drawing uses a scale where 14 inch\frac{1}{4}\text{ inch} represents 3 feet3\text{ feet}. What is the actual area of the community garden in square feet?

  1. A
    112.5112.5
  2. B
    150150
  3. C
    180180
  4. 1,8001,800Answer

Answer

The actual area of the community garden is 1,8001,800 square feet.
The correct answer is found by first establishing how many feet each inch on the layout represents. Since a quarter of an inch represents 3 feet, one full inch represents 12 feet (4 times 3). Multiplying the layout dimensions by 12 provides the actual dimensions: a width of 30 feet and a length of 60 feet. Finally, multiplying the actual width by the actual length (30 x 60) gives the true area of 1,800 square feet.

Step-by-Step Solution

1
Determine the unit scale factor for 1 inch.
Since 1/4 inch=3 feet1/4\text{ inch} = 3\text{ feet}, multiplying both sides by 4 gives 1 inch=12 feet1\text{ inch} = 12\text{ feet}.
Converting the scale to a 'per inch' rate makes it easier to apply to the drawing measurements.
2
Calculate the actual width and length of the garden.
Actual width = 2.5×12=30 feet2.5 \times 12 = 30\text{ feet}. Actual length = 5×12=60 feet5 \times 12 = 60\text{ feet}.
Applying the linear scale factor converts the map dimensions directly into real-world dimensions.
3
Calculate the area of the actual garden.
Area = 30 feet×60 feet=1,800 square feet30\text{ feet} \times 60\text{ feet} = 1,800\text{ square feet}.
The area of a rectangle is found by multiplying its length by its width.

Key Concept

Scale Drawings and Area Calculation
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Topics

Scale Drawings

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