Question
Given: The streets form a rectangle with a diagonal. The height is 4 and width is 3
Michael is training for a marathon and wants to run 15 miles. Which path should be take?
Michael is training for a marathon and wants to run 15 miles. Which path should be take?
Answers
Answered by
GPT-4o mini
To determine the best path for Michael to run 15 miles, we need to identify the dimensions of the rectangular area formed by the streets, which are 4 units high and 3 units wide. This forms a rectangle with a diagonal.
First, let's calculate the diagonal distance (D) of the rectangle using the Pythagorean theorem:
\[
D = \sqrt{(width^2 + height^2)} = \sqrt{(3^2 + 4^2)} = \sqrt{(9 + 16)} = \sqrt{25} = 5 \text{ units}
\]
With a rectangular layout where various paths are available, Michael can choose different routes to accumulate the total distance of 15 miles. To achieve this, he can utilize combinations of running along the perimeter, diagonally across the rectangle, or repeating laps around the rectangle.
**Calculating the Perimeter:**
The perimeter (P) of the rectangle can be calculated as:
\[
P = 2 \times (width + height) = 2 \times (3 + 4) = 2 \times 7 = 14 \text{ units}
\]
If Michael runs the perimeter, he can repeat laps to reach his goal of 15 miles. To convert units into miles, we need to clarify what these units represent. If we assume that each unit represents a mile, then running around the perimeter once would give him 14 miles, and he would need to run an additional mile to reach his goal of 15 miles.
### Suggested Path:
1. **Run around the perimeter of the rectangle once:** (14 miles)
2. **Run an additional mile along any side (or across the diagonal if applicable).**
### Conclusion:
Michael should run around the perimeter of the rectangle (14 miles) and then run an additional mile along one of the sides to complete his training for 15 miles. Alternatively, he could use combinations of heading towards the diagonal or repeat laps as needed, depending on his training strategy and the available path options.
First, let's calculate the diagonal distance (D) of the rectangle using the Pythagorean theorem:
\[
D = \sqrt{(width^2 + height^2)} = \sqrt{(3^2 + 4^2)} = \sqrt{(9 + 16)} = \sqrt{25} = 5 \text{ units}
\]
With a rectangular layout where various paths are available, Michael can choose different routes to accumulate the total distance of 15 miles. To achieve this, he can utilize combinations of running along the perimeter, diagonally across the rectangle, or repeating laps around the rectangle.
**Calculating the Perimeter:**
The perimeter (P) of the rectangle can be calculated as:
\[
P = 2 \times (width + height) = 2 \times (3 + 4) = 2 \times 7 = 14 \text{ units}
\]
If Michael runs the perimeter, he can repeat laps to reach his goal of 15 miles. To convert units into miles, we need to clarify what these units represent. If we assume that each unit represents a mile, then running around the perimeter once would give him 14 miles, and he would need to run an additional mile to reach his goal of 15 miles.
### Suggested Path:
1. **Run around the perimeter of the rectangle once:** (14 miles)
2. **Run an additional mile along any side (or across the diagonal if applicable).**
### Conclusion:
Michael should run around the perimeter of the rectangle (14 miles) and then run an additional mile along one of the sides to complete his training for 15 miles. Alternatively, he could use combinations of heading towards the diagonal or repeat laps as needed, depending on his training strategy and the available path options.