Question

Steffie makes a scale drawing of 1:3. The dimensions of her scale drawing are 15 inches long by 12 inches wide. The builder creates a scale drawing of the crate with a scale factor of 1:9. what are the dimensions of the builders scale drawing?

Answer 1

To find the dimensions of the builder's scale drawing based on Steffie's scale drawing, we first need to understand the scale factors involved.

Steffie's scale drawing is at a scale of 1:3, meaning that the dimensions of the actual crate are three times larger than the dimensions of her drawing.

Let’s calculate the actual dimensions of the crate using Steffie's drawing:

1. Length of the actual crate:
\[
\text{Actual Length} = \text{Length of drawing} \times \text{Scale Factor} = 15 \, \text{inches} \times 3 = 45 \, \text{inches}
\]

2. Width of the actual crate:
\[
\text{Actual Width} = \text{Width of drawing} \times \text{Scale Factor} = 12 \, \text{inches} \times 3 = 36 \, \text{inches}
\]

Now we have the actual dimensions of the crate: 45 inches long and 36 inches wide.

Next, the builder creates a scale drawing of the crate at a scale factor of 1:9. This means the drawing dimensions will be one-ninth of the actual dimensions:

1. Length of the builder’s scale drawing:
\[
\text{Builder's Length} = \frac{\text{Actual Length}}{9} = \frac{45 \, \text{inches}}{9} = 5 \, \text{inches}
\]

2. Width of the builder’s scale drawing:
\[
\text{Builder's Width} = \frac{\text{Actual Width}}{9} = \frac{36 \, \text{inches}}{9} = 4 \, \text{inches}
\]

Thus, the dimensions of the builder's scale drawing are **5 inches long by 4 inches wide**.