To find the actual length of Harper's bedroom, we need to determine the scale factor from the scale drawing to the actual dimensions.
The width of the house in the scale drawing is 4 inches, and the actual width is 30 feet.
First, we calculate the scale factor:
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Convert actual width from feet to inches: \[ 30 \text{ feet} \times 12 \text{ inches/foot} = 360 \text{ inches} \]
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Now we calculate the scale factor: \[ \text{Scale factor} = \frac{\text{Actual width}}{\text{Drawing width}} = \frac{360 \text{ inches}}{4 \text{ inches}} = 90 \]
This means that 1 inch on the drawing corresponds to 90 inches in reality.
Next, we use the scale factor to find the actual length of Harper's bedroom. The bedroom in the scale drawing measures 1.6 inches long.
To find its actual length: \[ \text{Actual length of bedroom} = \text{Length in drawing} \times \text{Scale factor} \] \[ \text{Actual length of bedroom} = 1.6 \text{ inches} \times 90 = 144 \text{ inches} \]
Finally, we convert the length from inches back to feet: \[ \text{Actual length in feet} = \frac{144 \text{ inches}}{12 \text{ inches/foot}} = 12 \text{ feet} \]
So, Harper's bedroom is \( \boxed{12} \) feet long.
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