The length and breadth of a room are 8 m and 6 m respectively. A cat runs…
2024
The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all four walls and finally along the diagonal, in order to catch a rat. What is the total distance covered by the cat?
- A.
10
- B.
13
- C.
38
- D.
48
Show answer & explanation
Correct answer: C
Concept: When a path goes around a rectangle's boundary and then along its diagonal, the total distance equals the perimeter of the rectangle plus the length of the diagonal. Because the diagonal splits the rectangle into two right triangles, its length is found using the Pythagorean theorem: diagonal = √(length2 + breadth2).
Application: Compute the perimeter and the diagonal separately, then add them.
Perimeter of the room = 2 × (length + breadth) = 2 × (8 + 6) = 28 m.
Diagonal = √(82 + 62) = √(64 + 36) = √100 = 10 m.
Total distance covered by the cat = perimeter + diagonal = 28 + 10 = 38 m.
Cross-check: 6, 8, 10 is a Pythagorean triple, so the diagonal is exactly 10 m with no rounding involved; this confirms 28 + 10 = 38 m as an exact total, matching only one of the given values.
