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Ari is designing a patio that will be 20 feet long and 16 feet wide. He makes a scale drawing of the patio using a scale of 1 inch to 4 feet.
 The ratio of the area of the scaled drawing to the actual area of the patio is 1 square inch to ?
 square feet.

First, let's calculate the actual area of the patio:

\[
\text{Actual Area} = \text{Length} \times \text{Width} = 20 \, \text{feet} \times 16 \, \text{feet} = 320 \, \text{square feet}
\]

Next, we need to determine the dimensions of the scaled drawing. Since the scale is 1 inch to 4 feet:

\[
\text{Scaled Length} = \frac{20 \, \text{feet}}{4 \, \text{feet per inch}} = 5 \, \text{inches}
\]
\[
\text{Scaled Width} = \frac{16 \, \text{feet}}{4 \, \text{feet per inch}} = 4 \, \text{inches}
\]

Now, calculate the area of the scaled drawing:

\[
\text{Scaled Area} = \text{Scaled Length} \times \text{Scaled Width} = 5 \, \text{inches} \times 4 \, \text{inches} = 20 \, \text{square inches}
\]

The ratio of the area of the scaled drawing to the actual area of the patio is:

\[
\frac{\text{Scaled Area}}{\text{Actual Area}} = \frac{20 \, \text{square inches}}{320 \, \text{square feet}}
\]

Simplify the ratio:

\[
\frac{20}{320} = \frac{1}{16}
\]

Therefore, the ratio of the area of the scaled drawing to the actual area of the patio is 1 square inch to 16 square feet.

The correct answer is:

\[
16
\]

Would you like more details or have any questions?

Here are 5 questions you might want to ask next:
1. How do you convert between different units of area?
2. What are some practical applications of scale drawings in real life?
3. How do you calculate the perimeter of a scaled drawing?
4

Explore how to calculate the ratio of the area of a scale drawing to the actual area using Ari's patio example. This problem involves understanding scale drawings, area calculations, and ratios. Suitable for students in Grades 6-8.

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