The cat covers a total distance of 38 m.

Step-by-step reasoning

  • Length of the room =8 m=8\text{ m}=8 m, breadth =6 m=6\text{ m}=6 m.
  • The cat first runs along all four walls , which is just the perimeter of the rectangle.
    • Perimeter =2×(8+6)=2×14=28 m=2\times (8+6)=2\times 14=28\text{ m}=2×(8+6)=2×14=28 m.
  • Then it runs along a diagonal of the room to catch the rat.
    • Diagonal of a rectangle =82+62=64+36=100=10 m=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10\text{ m}=82+62​=64+36​=100​=10 m.
  • Total distance covered
    • === distance along walls +++ diagonal
    • =28 m+10 m=38 m=28\text{ m}+10\text{ m}=38\text{ m}=28 m+10 m=38 m.

So, the cat finally runs 38 m in total to catch the rat.

Mini story twist

Imagine the room as a neat 8 m by 6 m arena , with the cat sprinting all the way around the edges like it’s tracing the boundary of a race track.

Just when the rat thinks it’s safe in the opposite corner, the cat cuts across the room in a straight diagonal dash —the shortest path between two opposite corners—adding that final 10 m burst to its chase.

TL;DR:
Perimeter of room =28 m=28\text{ m}=28 m, diagonal =10 m=10\text{ m}=10 m, total distance =38 m=38\text{ m}=38 m.

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