Question
A park is in a shape of a rectangle that is 9 kilometers long and 12 kilometers wide. A dog runs diagonally from one corner across the park to the other corner. Create a sketch to model the situation
Answers
Answered by
GPT-4o mini
While I can't create visual sketches, I can guide you on how to draw one based on the description provided.
**Steps to create a sketch:**
1. **Draw a rectangle**: Start by drawing a rectangle to represent the park. Make the length of the rectangle 9 kilometers and the width 12 kilometers. You can label the longer side (12 km) as "Width" and the shorter side (9 km) as "Length".
2. **Label the corners**: Label the corners of the rectangle as points \( A \), \( B \), \( C \), and \( D \):
- \( A \) (bottom left corner)
- \( B \) (bottom right corner)
- \( C \) (top right corner)
- \( D \) (top left corner)
3. **Draw the diagonal**: Draw a line from corner \( A \) to corner \( C \). This line represents the path that the dog takes running diagonally across the park.
4. **Label the diagonal**: You can label the diagonal line \( AC \) and you may also want to indicate that it represents the distance the dog runs.
5. **Optional**: You could also calculate the length of the diagonal using the Pythagorean theorem. The diagonal \( d \) can be calculated as:
\[
d = \sqrt{(length^2 + width^2)} = \sqrt{(9^2 + 12^2)} = \sqrt{(81 + 144)} = \sqrt{225} = 15 \text{ kilometers}
\]
You could write this as a note on your sketch.
By following these steps, you'll have a clear and informative diagram representing the dog’s run across the park.
**Steps to create a sketch:**
1. **Draw a rectangle**: Start by drawing a rectangle to represent the park. Make the length of the rectangle 9 kilometers and the width 12 kilometers. You can label the longer side (12 km) as "Width" and the shorter side (9 km) as "Length".
2. **Label the corners**: Label the corners of the rectangle as points \( A \), \( B \), \( C \), and \( D \):
- \( A \) (bottom left corner)
- \( B \) (bottom right corner)
- \( C \) (top right corner)
- \( D \) (top left corner)
3. **Draw the diagonal**: Draw a line from corner \( A \) to corner \( C \). This line represents the path that the dog takes running diagonally across the park.
4. **Label the diagonal**: You can label the diagonal line \( AC \) and you may also want to indicate that it represents the distance the dog runs.
5. **Optional**: You could also calculate the length of the diagonal using the Pythagorean theorem. The diagonal \( d \) can be calculated as:
\[
d = \sqrt{(length^2 + width^2)} = \sqrt{(9^2 + 12^2)} = \sqrt{(81 + 144)} = \sqrt{225} = 15 \text{ kilometers}
\]
You could write this as a note on your sketch.
By following these steps, you'll have a clear and informative diagram representing the dog’s run across the park.