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Question

Length and Area in Scale Drawings Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the 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 first need to determine the scale factor based on the original dimensions of the rectangle.

The original width of the rectangle is 12 inches, and Spencer wants the new width to be 1.5 inches. We can find the scale factor by dividing the new width by the original width:

\[ \text{Scale factor} = \frac{\text{New width}}{\text{Original width}} = \frac{1.5}{12} \]

Calculating the scale factor:

\[ \frac{1.5}{12} = \frac{1.5 \div 1.5}{12 \div 1.5} = \frac{1}{8} \]

This means that Spencer's new drawing is 1/8 of the size of the original drawing.

Next, we apply this scale factor to the original length of the rectangle:

\[ \text{Original length} = 20 \text{ inches} \]

Using the scale factor to find the new length:

\[ \text{New length} = \text{Original length} \times \text{Scale factor} = 20 \times \frac{1}{8} = 20 \div 8 = 2.5 \text{ inches} \]

Therefore, the length of the rectangle in Spencer's new scale drawing is 2.5 inches.