Question
A rectangle shows a length measuring 20 inches and width measuring 12 inches.
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.
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.
Answers
GPT-4o mini
To solve for the length of Spencer's new scale drawing, we first need to find the scale factor based on the original rectangle's dimensions and the new width.
The original rectangle has the following dimensions:
- Length = 20 inches
- Width = 12 inches
Spencer wants to create a smaller scale drawing where the width is 1.5 inches. We can calculate the scale factor by comparing the new width to the original width:
\[
\text{Scale factor} = \frac{\text{New width}}{\text{Original width}} = \frac{1.5 \text{ inches}}{12 \text{ inches}} = \frac{1.5}{12} = \frac{1}{8}
\]
Now that we have the scale factor, we apply it to the original length to find the new length in the scaled drawing:
\[
\text{New length} = \text{Original length} \times \text{Scale factor} = 20 \text{ inches} \times \frac{1}{8}
\]
\[
\text{New length} = 20 \times 0.125 = 2.5 \text{ inches}
\]
Thus, the length of the rectangle in Spencer's new scale drawing will be **2.5 inches**.
The original rectangle has the following dimensions:
- Length = 20 inches
- Width = 12 inches
Spencer wants to create a smaller scale drawing where the width is 1.5 inches. We can calculate the scale factor by comparing the new width to the original width:
\[
\text{Scale factor} = \frac{\text{New width}}{\text{Original width}} = \frac{1.5 \text{ inches}}{12 \text{ inches}} = \frac{1.5}{12} = \frac{1}{8}
\]
Now that we have the scale factor, we apply it to the original length to find the new length in the scaled drawing:
\[
\text{New length} = \text{Original length} \times \text{Scale factor} = 20 \text{ inches} \times \frac{1}{8}
\]
\[
\text{New length} = 20 \times 0.125 = 2.5 \text{ inches}
\]
Thus, the length of the rectangle in Spencer's new scale drawing will be **2.5 inches**.