Example 20: Mrs. Barron’s kitchen is shaped like a rectangle. She has a scale drawing of her kitchen with dimensions 6 inches by 4 inches. The scale of the drawing is 1 1/2
inch = 1 foot. What is the perimeter of Mrs. Barron’s actual kitchen?
The Correct Answer and Explanation is:
To find the actual dimensions of Mrs. Barron’s kitchen, it is necessary to understand and apply the given scale properly. The drawing shows a rectangle measuring 6 inches by 4 inches, and the scale provided is 1½ inches = 1 foot.
Step 1: Interpret the scale
The scale “1½ inches = 1 foot” means that every 1.5 inches in the drawing represents 1 real-life foot.
Step 2: Calculate the actual length
The longer side of the rectangle in the drawing is 6 inches.
To convert this to feet, divide the drawing length by the scale factor:
6 inches ÷ 1.5 inches per foot = 4 feet.
Step 3: Calculate the actual width
The shorter side of the rectangle in the drawing is 4 inches.
4 inches ÷ 1.5 inches per foot = 2.67 feet (which is approximately 2 feet and 8 inches).
Final Answer:
The actual dimensions of the kitchen are 4 feet by approximately 2.67 feet.
Explanation
Understanding scale drawings is crucial when interpreting blueprints or diagrams used in architecture and design. A scale drawing represents a real object with accurate sizes reduced or enlarged by a certain ratio. In this case, the ratio is 1½ inches to 1 foot. That means for every 1½ inches measured in the drawing, the corresponding real-life dimension is 1 foot.
To determine the actual size, convert the drawing’s dimensions using the scale. For the length, 6 inches from the drawing represents how many feet in reality? This can be found by dividing the drawing measurement (6 inches) by the scale unit (1.5 inches). The result is 4, meaning the real kitchen length is 4 feet. The same method applies to the width. Divide 4 inches by 1.5 inches, which gives approximately 2.67 feet. Since one foot equals 12 inches, 0.67 feet is close to 8 inches (0.67 × 12 = 8.04 inches).
This conversion ensures accurate understanding of space during planning. Precision in using scales ensures designs reflect true proportions, which is essential for proper construction, appliance fitting, and interior planning. Mistakes in scale interpretation may lead to significant structural or design errors. In summary, interpreting scale ratios correctly is essential for translating blueprint measurements into real-world dimensions, ensuring that physical spaces match the intended design accurately.
