To determine the dimensions of the scale drawing, we need to apply the given scale factor to the original dimensions of the rectangle.
1. Identify the original dimensions of the rectangle:
- The original length is 12 inches.
- The original width is 8 inches.
2. Understand the scale factor:
- The scale factor is [tex]\(\frac{2}{3}\)[/tex].
3. Calculate the scaled length:
- Multiply the original length by the scale factor:
[tex]\[
\text{scaled length} = \text{original length} \times \text{scale factor} = 12 \times \frac{2}{3}
\][/tex]
- Perform the multiplication:
[tex]\[
12 \times \frac{2}{3} = 8
\][/tex]
- The scaled length is 8 inches.
4. Calculate the scaled width:
- Multiply the original width by the scale factor:
[tex]\[
\text{scaled width} = \text{original width} \times \text{scale factor} = 8 \times \frac{2}{3}
\][/tex]
- Perform the multiplication:
[tex]\[
8 \times \frac{2}{3} \approx 5.333
\][/tex]
- The scaled width is approximately 5.33 inches (or [tex]\(\frac{16}{3}\)[/tex]).
So, the dimensions of the scale drawing are:
- Length: 8 inches
- Width: approximately 5.33 inches
