Think About the Process The scale for the drawing of a rectangular playing field is 2 inchesequals5 feet. Find an equation you can use to find the dimensions of the actual field. What are the actual​ dimensions?

Question

length
width
8 in.
4 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 relate the dimensions of the scale drawing to the actual dimensions of the rectangular playing field, we can use the given scale of 2 inches equals 5 feet.

First, let's express this relationship mathematically. If \( x \) represents a dimension in inches (the scale drawing), we need to determine the equation relating \( x \) to the actual dimension \( y \) in feet.

Given that 2 inches corresponds to 5 feet, we can set up the proportion as follows:

\[ \frac{2 \text{ inches}}{5 \text{ feet}} = \frac{x \text{ inches}}{y \text{ feet}} \]

Cross-multiplying gives us:

\[ 2y = 5x \]

To find \( y \), we can solve for \( y \):

\[ y = \frac{5}{2}x \]

Thus, the equation you can use to find the dimensions of the actual field is:

\[ y = \frac{5}{2} x \]

Part 2: Finding the Actual Dimensions

Now, we can substitute the scale dimensions of the drawing:

1. For the length:

   • If the length in the drawing is \( 8 \) inches, we can find the actual length \( y \): \[ y = \frac{5}{2} \times 8 = \frac{5 \times 8}{2} = 20 \text{ feet} \]

2. For the width:

   • If the width in the drawing is \( 4 \) inches, we can find the actual width \( y \): \[ y = \frac{5}{2} \times 4 = \frac{5 \times 4}{2} = 10 \text{ feet} \]

Summary

• The equation relating the scale drawing to the actual dimensions is: \[ y = \frac{5}{2} x \]

• The actual dimensions of the field are:

  • Length: 20 feet
  • Width: 10 feet