Question

Toby drew a scale drawing of a county park. The scale he used was 5 inches = 1 yard. What is the drawing's scale factor?

Simplify your answer and write it as a ratio, using a colon.

Answer 1

To find the scale factor in a drawing, you can compare the measurement on the drawing to the actual measurement. Here, Toby's scale is given as 5 inches representing 1 yard.

First, convert yards to inches because the units need to be the same for a proper ratio. Since 1 yard equals 36 inches, we can express the scale as:

\[
5 \text{ inches} = 1 \text{ yard} = 36 \text{ inches}
\]

Now, we can establish the ratio of drawing measurement to actual measurement:

\[
\text{Scale factor} = \frac{\text{Drawing measurement}}{\text{Actual measurement}} = \frac{5 \text{ inches}}{36 \text{ inches}}
\]

To simplify this ratio, we can use the scale factor directly:

\[
\frac{5}{36}
\]

Thus, the scale factor in ratio form is:

\[
5 : 36
\]

Therefore, the drawing's scale factor is **5:36**.