To determine the scale the architect used, we need to find out how many inches in reality corresponds to the 1/4 inch representation in the scale drawing.
The model height (represented on the drawing) is 1/4 inch, and it corresponds to a real-life height of 9 inches.
To find the scale, we can set up the following proportion:
\[ \text{Scale Factor} = \frac{\text{Actual Height}}{\text{Drawing Height}} = \frac{9 \text{ inches}}{\frac{1}{4} \text{ inch}} \]
Calculating this gives:
\[ \text{Scale Factor} = 9 \times 4 = 36 \]
This means that for every 1 inch on the drawing, it represents 36 inches in reality.
Next, we need to convert this into feet since the options are given in feet. There are 12 inches in a foot, therefore:
\[ 36 \text{ inches} = \frac{36}{12} \text{ feet} = 3 \text{ feet} \]
We can express this scale as follows:
1 inch on the drawing represents 3 feet in reality, meaning:
\[ 1 \text{ foot} = \frac{1}{3} \text{ inch} \]
This indicates that the correct answer aligns with the option:
1 foot = 1/3 inch.
Thus, the architect used a scale of 1 foot = 1/3 inch.
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