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.