To solve the question of finding the scale factor for a scale drawing that has a scale of [tex]\(3 \text{ inches}: 1 \text{ foot}\)[/tex], we can follow these steps:
1. Understand the given scale:
The scale provided is [tex]\(3 \text{ inches} : 1 \text{ foot}\)[/tex]. This means that 3 inches on the drawing represent 1 foot in real life.
2. Convert feet to inches:
Since the scale involves different units (inches and feet), we need to express both quantities in the same unit. We know that:
[tex]\[
1 \text{ foot} = 12 \text{ inches}
\][/tex]
So, we convert 1 foot to inches:
[tex]\[
1 \text{ foot} = 12 \text{ inches}
\][/tex]
3. Express the scale in consistent units:
Now that we have converted 1 foot to 12 inches, we can restate the given scale entirely in inches. Therefore, the scale [tex]\(3 \text{ inches}: 1 \text{ foot}\)[/tex] becomes:
[tex]\[
3 \text{ inches}: 12 \text{ inches}
\][/tex]
4. Calculate the scale factor:
A scale factor compares the length on the drawing to the corresponding length in real life in the same unit. The scale factor can be calculated as follows:
[tex]\[
\text{Scale Factor} = \frac{\text{Length on drawing}}{\text{Actual length}}
\][/tex]
Substituting the given and converted values:
[tex]\[
\text{Scale Factor} = \frac{3 \text{ inches}}{12 \text{ inches}} = \frac{3}{12} = 0.25
\][/tex]
Therefore, the scale factor for the drawing is [tex]\(0.25\)[/tex].
