Question

Eli measured a house and its lot and made a scale drawing. He used the scale 4 inches = 3 feet. What is the drawing's scale factor?

Simplify your answer and write it as a fraction.

Answer 1

The scale given is 4 inches = 3 feet. To express this as a scale factor, we need to convert both quantities to the same unit.

First, we'll convert 3 feet to inches. Since there are 12 inches in a foot:

\[
3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches}
\]

Now we have the scale in inches:

\[
4 \text{ inches} = 36 \text{ inches}
\]

To find the scale factor, we set up the ratio of the drawing measurement to the actual measurement:

\[
\text{Scale factor} = \frac{\text{Drawing}}{\text{Actual}} = \frac{4 \text{ inches}}{36 \text{ inches}}
\]

Now, we can simplify this fraction:

\[
\frac{4}{36} = \frac{1}{9} \quad (\text{dividing both numerator and denominator by 4})
\]

Thus, the drawing's scale factor is:

\[
\boxed{\frac{1}{9}}
\]