Use the image to answer the question.

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.

(1 point)
___inches

Answer 1

To find the length of the rectangle in Spencer's new scale drawing, we can use the relationship between the original rectangle's dimensions and the desired width of the new drawing.

The original dimensions are:

• Length: 20 inches
• Width: 12 inches

In the smaller scale drawing, the new width is 1.5 inches. We can set up a proportion based on the original and new widths to find the new length.

Let's denote the new length as \( L \).

The relationship between the original and new dimensions can be expressed as follows:

\[ \frac{\text{new width}}{\text{original width}} = \frac{\text{new length}}{\text{original length}} \]

Substituting in the values we have:

\[ \frac{1.5}{12} = \frac{L}{20} \]

Cross-multiplying gives:

\[ 1.5 \times 20 = 12 \times L \]

Calculating the left side:

\[ 30 = 12L \]

Now, solve for \( L \):

\[ L = \frac{30}{12} = 2.5 \]

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

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