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

The dimensions of the original rectangle are:

• Length = 20 inches
• Width = 12 inches

The scale drawing has a width of 1.5 inches. To find the scale factor, we compare 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, we will apply this scale factor to the original length to find the new length in Spencer's drawing:

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

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