Question
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
12 in.
6 in.
Find an equation you can use to find the dimensions of the actual field.
Use the equation y= __x, where x is a dimension of the scale drawing (in inches) and y is the corresponding dimension of the actual field (in feet).
length
width
12 in.
6 in.
Find an equation you can use to find the dimensions of the actual field.
Use the equation y= __x, where x is a dimension of the scale drawing (in inches) and y is the corresponding dimension of the actual field (in feet).
Answers
GPT-4o mini
To derive an equation that connects the dimensions from the scale drawing to the actual dimensions of the rectangular playing field, we start with the given scale: 2 inches on the drawing corresponds to 3 feet in reality.
We can find the conversion factor by setting up a proportion based on the scale:
\[
\frac{\text{actual feet}}{\text{drawing inches}} = \frac{3 \text{ feet}}{2 \text{ inches}}.
\]
To find the relationship between the dimensions of the scale drawing (in inches) and the actual dimensions of the field (in feet), we can express it in the form \(y = mx\), where:
- \(y\) is the actual dimension in feet,
- \(x\) is the dimension in inches,
- \(m\) is the conversion factor.
From the scale, we can see that:
\[
m = \frac{3 \text{ feet}}{2 \text{ inches}} = 1.5 \text{ feet per inch}.
\]
Thus, the equation that relates the dimension in inches to the actual dimension in feet is:
\[
y = 1.5x.
\]
Next, we can use this equation to find the actual dimensions of the playing field given its dimensions from the scale drawing:
- Length from the drawing: \(12\) inches
- Width from the drawing: \(6\) inches
Now we can calculate the actual length and width using the equation \(y = 1.5x\).
1. **Actual Length**:
\[
y = 1.5 \times 12 = 18 \text{ feet}.
\]
2. **Actual Width**:
\[
y = 1.5 \times 6 = 9 \text{ feet}.
\]
**Final Answer**:
- The equation is \(y = 1.5x\).
- Actual Length: **18 feet**.
- Actual Width: **9 feet**.
We can find the conversion factor by setting up a proportion based on the scale:
\[
\frac{\text{actual feet}}{\text{drawing inches}} = \frac{3 \text{ feet}}{2 \text{ inches}}.
\]
To find the relationship between the dimensions of the scale drawing (in inches) and the actual dimensions of the field (in feet), we can express it in the form \(y = mx\), where:
- \(y\) is the actual dimension in feet,
- \(x\) is the dimension in inches,
- \(m\) is the conversion factor.
From the scale, we can see that:
\[
m = \frac{3 \text{ feet}}{2 \text{ inches}} = 1.5 \text{ feet per inch}.
\]
Thus, the equation that relates the dimension in inches to the actual dimension in feet is:
\[
y = 1.5x.
\]
Next, we can use this equation to find the actual dimensions of the playing field given its dimensions from the scale drawing:
- Length from the drawing: \(12\) inches
- Width from the drawing: \(6\) inches
Now we can calculate the actual length and width using the equation \(y = 1.5x\).
1. **Actual Length**:
\[
y = 1.5 \times 12 = 18 \text{ feet}.
\]
2. **Actual Width**:
\[
y = 1.5 \times 6 = 9 \text{ feet}.
\]
**Final Answer**:
- The equation is \(y = 1.5x\).
- Actual Length: **18 feet**.
- Actual Width: **9 feet**.