Math Problem Statement

Type the correct answer in the box. Use numerals instead of words. Masha is making a scale diagram of the front face of an aquarium. The face is shaped like a rectangle. She uses a scale of 1 centimeter to 6 inches to draw the diagram. The actual length of the aquarium face is 5 feet, and its width is 2 feet. The perimeter of the scale drawing of the front face is centimeters.

Solution

To find the perimeter of the scale drawing of the front face of the aquarium, we first need to convert the actual dimensions to the scale dimensions using the given scale of 1 centimeter to 6 inches.

Conversion factors:

1 foot = 12 inches

Actual dimensions in inches:

  • Length: 5feet×12inches/foot=60inches5 \, \text{feet} \times 12 \, \text{inches/foot} = 60 \, \text{inches}
  • Width: 2feet×12inches/foot=24inches2 \, \text{feet} \times 12 \, \text{inches/foot} = 24 \, \text{inches}

Scale dimensions:

Since 1 centimeter on the scale drawing corresponds to 6 inches of the actual dimensions:

  • Scale length: 60inches6inches/cm=10cm\frac{60 \, \text{inches}}{6 \, \text{inches/cm}} = 10 \, \text{cm}
  • Scale width: 24inches6inches/cm=4cm\frac{24 \, \text{inches}}{6 \, \text{inches/cm}} = 4 \, \text{cm}

Perimeter of the scale drawing:

The formula for the perimeter of a rectangle is: Perimeter=2×(Length+Width)\text{Perimeter} = 2 \times (\text{Length} + \text{Width})

Substitute the scale dimensions: Perimeter=2×(10cm+4cm)=2×14cm=28cm\text{Perimeter} = 2 \times (10 \, \text{cm} + 4 \, \text{cm}) = 2 \times 14 \, \text{cm} = 28 \, \text{cm}

Therefore, the perimeter of the scale drawing of the front face is 28\boxed{28} centimeters.

Do you want details or have any questions?

Here are 5 questions you can ask next:

  1. How do you calculate the area of a scale drawing from the actual area?
  2. What is the process to convert different units of measurement in a scale diagram?
  3. Can you explain the difference between perimeter and area calculations?
  4. How can scale drawings be used in real-life planning, such as architecture?
  5. What steps should be taken to ensure accuracy when creating a scale drawing?

Tip: When converting measurements for scale drawings, always ensure that all units are consistent to avoid errors in the calculations.

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Math Problem Analysis

Mathematical Concepts

Scale drawings
Unit conversion
Perimeter of rectangles

Formulas

Perimeter of a rectangle: 2 * (Length + Width)

Theorems

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Suitable Grade Level

Grades 6-8