Question

Spencer draws a rectangle to represent the size of the city block where he lives. The rectangle is labeled in inches. Spencer decides he wants to make a smaller scale drawing of the rectangle in which the width is just 1.5 inches long. What will be the length of the rectangle in Spencer's new scale drawing? Write your answer in decimal form.

On the left side of the rectangle is the measurement 12ft. On the top of the rectangle is the measurement of 20 ft

Answer 1

To find the length of the rectangle in Spencer's new scale drawing, we need to first determine the scale factor based on the original dimensions of the rectangle.

1. **Convert the original dimensions to inches:**
- The original width is 12 ft, which is equivalent to \( 12 \times 12 = 144 \) inches.
- The original length is 20 ft, which is equivalent to \( 20 \times 12 = 240 \) inches.

2. **Determine the scale factor:**
The original width of the rectangle is 144 inches, and the new width needs to be 1.5 inches. Therefore, the scale factor can be calculated as follows:

\[
\text{Scale factor} = \frac{\text{new width}}{\text{original width}} = \frac{1.5 \text{ in}}{144 \text{ in}} = \frac{1.5}{144} = \frac{1}{96}
\]

3. **Apply the scale factor to the original length:**
The original length is 240 inches. To find the new length in the scaled drawing:

\[
\text{New length} = \text{original length} \times \text{scale factor} = 240 \text{ in} \times \frac{1}{96}
\]

Now calculate \( 240 \div 96 \):

\[
240 \div 96 = 2.5
\]

Thus, the length of the rectangle in Spencer's new scale drawing is:

\[
\boxed{2.5} \text{ inches}
\]