To find the scale factor of Tucker's drawing of the office building, we start with the scale provided: 2 inches = 6 feet.
First, we need to express both measurements in the same units. Let's convert 6 feet to inches because there are 12 inches in a foot:
6 feet × 12 inches/foot = 72 inches.
Now we can write the scale relation using the two measurements, both in inches:
2 inches = 72 inches.
Now, we can find the scale factor by simplifying the ratio:
\[ \text{Scale factor} = \frac{2 \text{ inches}}{72 \text{ inches}} = \frac{2}{72}. \]
To simplify \(\frac{2}{72}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{2 \div 2}{72 \div 2} = \frac{1}{36}. \]
Thus, the scale factor can be written as a ratio of 1:36.
Therefore, the drawing's scale factor is:
1:36.
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