Question
Tucker made a scale drawing of an office building. The scale of the drawing was 2 inches = 6 feet. What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Simplify your answer and write it as a ratio, using a colon.
Answers
GPT-4o mini
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**.
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**.