The problem provided involves modeling a triangular path to calculate the total jogging distance. Here's the breakdown:

Given:

• A triangular route with vertices labeled as Pear Street, Plum Street, and Cherry Street.
• Distances provided:
  • One side of the triangle (Cherry Street to Plum Street) = 1.3 miles.
  • Another side (Plum Street to Pear Street) = 2.25 miles.

Task:

Calculate the total jogging distance, considering the route as follows:

• From Cherry Street to Plum Street.
• From Plum Street to Pear Street.
• From Pear Street back to Cherry Street.

This forms a closed triangular loop.

Solution:

The total jogging distance is the perimeter of the triangle: $\text{Total Distance} = \text{Side 1} + \text{Side 2} + \text{Side 3}.$

Missing Information:

We need the third side of the triangle (from Pear Street to Cherry Street) to complete the calculation. This third side forms the hypotenuse of a right triangle.

Using the Pythagorean Theorem:

The two given legs of the right triangle are:

• Base = 1.3 miles.
• Height = 2.25 miles.

The hypotenuse can be calculated as: $\text{Hypotenuse} = \sqrt{\text{Base}^2 + \text{Height}^2}.$

Substitute the values: $\text{Hypotenuse} = \sqrt{(1.3)^2 + (2.25)^2}.$ $\text{Hypotenuse} = \sqrt{1.69 + 5.0625} = \sqrt{6.7525} \approx 2.6 \, \text{miles}.$

Total Distance:

Now add all the sides: $\text{Total Distance} = 1.3 + 2.25 + 2.6 = 6.15 \, \text{miles}.$

Final Answer:

The total jogging distance is approximately 6.15 miles.

Would you like me to explain any part of this in more detail? Or confirm additional calculations?

5 Related Questions:

1. How can the Pythagorean theorem be used in real-world applications besides jogging routes?
2. What is the importance of modeling situations with right triangles?
3. How does rounding impact the accuracy of solutions in such scenarios?
4. What other methods could be used to determine distances in a triangular path?
5. How can trigonometry extend this problem to non-right triangles?

Tip:

Always double-check units in problems involving distance to ensure consistency throughout calculations.