Page 133: Matha Pachchi & Deep Dive

Matha Pachchi: Akshi vs Toshi

Scenario:

• Akshi’s Track (Outer): Rectangle $70\text{ m} \times 40\text{ m}$.
• Toshi’s Track (Inner): Rectangle $60\text{ m} \times 30\text{ m}$.

1. Total distance Akshi covered in 5 rounds:

2. Total distance Toshi covered in 7 rounds:

Conclusion: Toshi ran a longer distance ($1260 > 1100$).

Deep Dive (Page 134)

Problem: Two square tracks, Inner (100m side) and Outer (150m side). Common finish line. Race length is 350m. Where should they start?

Analysis:

• Race distance needed: 350 m.
• The finish line is in the middle of a side. Let’s analyze the path backwards from the finish line.
• Inner Runner (A):
  • Side length = 100 m.
  • Path to finish: Half side (50m) + Full Side (100m) + Full Side (100m) + Full Side (100m) = 350m.
  • This means runner A starts exactly at the finish line (completes exactly 1 round minus 50m? No, $350 = 3.5 \times 100$).
  • Actually, let’s look at the solution provided: “From point A to flag: $100+100+100+50 = 350$”. This implies starting at a corner or specific point.
• Outer Runner (B):
  • Side length = 150 m.
  • Path: $75 \text{ (half side)} + 150 + 125$?
  • Solution says: $125 + 150 + 75 = 350$.
  • $75$ is the final stretch (half side). $150$ is one full side. $125$ is the start of the side ($150 - 25$?).
  • Actually, $125 + 150 + 75 = 350$. This means they run 1 full side ($150$), one half side ($75$) to finish, and start $125$m back.

Akshi vs Toshi Triangle Debate (Page 134)

• Akshi: Perimeter is 9 units.
• Toshi: It’s more than 9 units.
• Reasoning: The diagonal of a square is longer than its side. The “slanted” lines in the triangle on the grid are diagonals of the grid squares. Their length is greater than 1 unit. Therefore, the sum is greater than just counting grid lines. Toshi is correct.