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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.

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inches
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1 answer

To find the length of the rectangle in Spencer's new scale drawing, we first need to determine the scale factor used in his drawing compared to the original rectangle.

The original dimensions of the rectangle are:

  • Length = 20 inches
  • Width = 12 inches

Spencer wants the new width to be 1.5 inches. We can find the scale factor by comparing the new width to the original width:

\[ \text{Scale Factor} = \frac{\text{New Width}}{\text{Original Width}} = \frac{1.5 \text{ inches}}{12 \text{ inches}} = \frac{1.5}{12} = \frac{1}{8} \]

This means that Spencer's new drawing is at a scale of \(\frac{1}{8}\) of the original size.

Now, we apply this scale factor to the original length to find the new length:

\[ \text{New Length} = \text{Original Length} \times \text{Scale Factor} = 20 \text{ inches} \times \frac{1}{8} = \frac{20}{8} = 2.5 \text{ inches} \]

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

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