On the blueprints of their new​ home, Paul and Gretha notice the balcony is 9 inches long and 4 inches wide. They know that the actual balcony will be 11.7 ft long. How wide will the balcony​ be?

Question

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Part 1
The width of the balcony will be
  
enter your response here ft. ​(Type a whole number or a​ decimal.)

Answer 1

To find the actual width of the balcony, we first need to determine the scale factor between the blueprint dimensions and the actual dimensions.

1. Calculate the scale factor based on the length:

   • Blueprint length: 9 inches
   • Actual length: 11.7 feet (we need to convert this to inches for consistency)
   • 11.7 feet = 11.7 × 12 = 140.4 inches

2. Determine the scale factor: \[ \text{Scale factor} = \frac{\text{Actual length}}{\text{Blueprint length}} = \frac{140.4 \text{ inches}}{9 \text{ inches}} \approx 15.6 \]

3. Apply the scale factor to the width:

   • Blueprint width: 4 inches
   • Actual width = Blueprint width × Scale factor \[ \text{Actual width} = 4 \text{ inches} \times 15.6 \approx 62.4 \text{ inches} \]

4. Convert the actual width to feet: \[ \text{Actual width in feet} = \frac{62.4 \text{ inches}}{12} \approx 5.2 \text{ feet} \]

Thus, the width of the balcony will be approximately 5.2 ft.