The length and breadth of a rectangular room are 8 m and 6 m respectively. A cat runs once along all four walls of the room (around the perimeter) and finally runs along one of the diagonals to catch a rat. What is the total distance covered by the cat?

Introduction:
This is a distance and geometry problem presented in a direction–sense context. We are told the dimensions of a rectangular room and that a cat runs around the four walls (the perimeter) and then along a diagonal of the room. The task is to compute the total distance travelled by the cat, which involves both perimeter and diagonal calculations for a rectangle.

Given Data / Assumptions:
• The room is rectangular with length 8 m and breadth 6 m.• The cat runs along all four walls, meaning along the entire perimeter once.• Then the cat runs along a diagonal of the room.• We assume the room is perfectly rectangular and that the diagonal connects two opposite corners.

Concept / Approach:
The total distance is the sum of the perimeter of the rectangle and the length of one diagonal. For a rectangle with length L and breadth B, the perimeter is 2 * (L + B). The diagonal can be found using the Pythagorean theorem because the diagonal, length and breadth form a right-angled triangle. Specifically, diagonal = sqrt(L^2 + B^2). Once we compute these two quantities, adding them gives the required total distance.

Step-by-Step Solution:
Step 1: Compute the perimeter of the room. With length L = 8 m and breadth B = 6 m, the perimeter P is:P = 2 * (L + B) = 2 * (8 + 6) = 2 * 14 = 28 m.Step 2: Compute the diagonal using the Pythagorean theorem:Diagonal = sqrt(L^2 + B^2) = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 m.Step 3: Add the perimeter distance and the diagonal distance to get the total distance the cat covers:Total distance = perimeter + diagonal = 28 + 10 = 38 m.

Verification / Alternative check:
We can check our calculations by observing that 8–6–10 is a well-known Pythagorean triplet similar to the classic 3–4–5 triangle, just scaled up by a factor of 2. Therefore, a rectangle with sides 8 and 6 must indeed have a diagonal of 10 m. The perimeter formula 2 * (8 + 6) is straightforward, so the arithmetic is reliable. Hence, 38 m is confidently the correct total distance.

Why Other Options Are Wrong:
The diagonal alone is 10 m, so 10 cannot be the total distance because the cat also runs along the walls. The perimeter alone is 28 m, so 34 and 14 are also too small or incorrectly derived. A value of 48 m would correspond to adding another 10 m or miscalculating the perimeter, perhaps as 38 m, but correct calculations do not support this. Only 38 m fits the correct sum of perimeter and diagonal.

Common Pitfalls:
Some students misread "runs along all the four walls" as running twice around the perimeter or only along two adjacent walls. Others incorrectly calculate the diagonal using L + B or some other non-Pythagorean expression. Remember that diagonals in rectangles always use the formula sqrt(L^2 + B^2), and that one full lap along four walls is simply the perimeter.

Final Answer:
The cat covers a total distance of 38 metres.