Question

Think About the Process  The scale for the drawing of a rectangular playing field is 2 inchesequals3 feet. Find an equation you can use to find the dimensions of the actual field. What are the actual​ dimensions?
length
width
24 in.
12 in.
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Part 1
Find an equation you can use to find the dimensions of the actual field.
Use the equation yequals
  
enter your response here​x, where x is a dimension of the scale drawing​ (in inches) and y is the corresponding dimension of the actual field​ (in feet).

Answer 1

To find the equation that relates the dimensions of the scale drawing (in inches) to the actual dimensions of the field (in feet), we need to account for the scale ratio given: 2 inches equals 3 feet.

We can write the equation as:
\[
y = \frac{3}{2} x
\]
where:
- \( y \) is the actual dimension of the field in feet,
- \( x \) is the dimension of the scale drawing in inches.

### Calculation of Actual Dimensions

Given the dimensions of the drawing:
- Length = 24 inches
- Width = 12 inches

#### Actual Length Calculation

Using the equation for length:
\[
y = \frac{3}{2} \times 24
\]
\[
y = \frac{3 \times 24}{2} = \frac{72}{2} = 36 \text{ feet}
\]

#### Actual Width Calculation

Using the equation for width:
\[
y = \frac{3}{2} \times 12
\]
\[
y = \frac{3 \times 12}{2} = \frac{36}{2} = 18 \text{ feet}
\]

### Summary of Actual Dimensions
- **Actual Length:** 36 feet
- **Actual Width:** 18 feet

So the final equation for the dimensions is \( y = \frac{3}{2} x \), and the actual dimensions of the field are 36 feet in length and 18 feet in width.