In a scale drawing of a house, 1 inch represents 5 feet. (a) In the scale drawing, the height of the house is 8 inches. What is the height of the real house? (b) The length of the... In a scale drawing of a house, 1 inch represents 5 feet. (a) In the scale drawing, the height of the house is 8 inches. What is the height of the real house? (b) The length of the real house is 35 feet. What is the length of the house in the scale drawing?
Understand the Problem
The question is asking us to find the dimensions of a house based on a scale drawing. In part (a), we need to convert the height of the house from inches in the drawing to feet in reality using the given scale. In part (b), we need to convert the length of the real house into inches in the scale drawing.
Answer
(a) $40$ feet; (b) $7$ inches
Answer for screen readers
(a) The height of the real house is 40 feet.
(b) The length of the house in the scale drawing is 7 inches.
Steps to Solve
- Convert height from inches to feet
To convert the height of the house from the drawing to the real height, use the scale provided. Given that 1 inch represents 5 feet:
$$ \text{Real height} = \text{Height in drawing} \times \text{Scale factor} $$
Here, the height in the drawing is 8 inches, so:
$$ \text{Real height} = 8 \text{ inches} \times 5 \text{ feet/inch} $$
- Perform the calculation for part (a)
Calculating the real height:
$$ \text{Real height} = 8 \times 5 = 40 \text{ feet} $$
- Convert length from feet to inches
For part (b), to find the length of the house in the scale drawing given that the real length is 35 feet, use the inverse of the scale:
$$ \text{Length in drawing} = \frac{\text{Real length}}{\text{Scale factor}} $$
Here, the scale factor remains the same:
$$ \text{Length in drawing} = \frac{35 \text{ feet}}{5 \text{ feet/inch}} $$
- Perform the calculation for part (b)
Calculating the length in the drawing:
$$ \text{Length in drawing} = \frac{35}{5} = 7 \text{ inches} $$
(a) The height of the real house is 40 feet.
(b) The length of the house in the scale drawing is 7 inches.
More Information
In a scale drawing, converting dimensions between real life and drawings is essential for accurate representation. Understanding and applying scale factors helps in a variety of fields, including architecture and design.
Tips
- Confusing the scale factor when converting dimensions.
- Forgetting to multiply when moving from the drawing to the real dimensions or vice versa.
- Incorrect addition or multiplication leading to erroneous final answers.
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