Q. The length and breadth of a room are 8 meters and 6 meters respectively. Tom runs along all the four walls and finally along a diagonal in order to catch Jerry. How much total distance is covered by Tom?

Q. The length and breadth of a room are 8 meters and 6 meters respectively. Tom runs along all the four walls and finally along a diagonal in order to catch Jerry. How much total distance is covered by Tom?

(ADRE 2024)

(A) 38 meters

(B) 10 meters

(C) 14 meters

(D) 28 meters

Answer:- (A) 38 meters

Solution:- 

To solve this, let’s break down Tom’s journey:

Distance covered along the walls:

• We know that the perimeter of a rectangle is the total distance of all four sides of a rectangle.
• This means Tom covers the perimeter of the room.
• Perimeter, $P=2\times (\text{Length}+\text{Breadth})$$$
• Therefore, $P=2\times (8+6)=2\times 14=28$ meters

Distance covered along the diagonal:

• The diagonal can be found using the Pythagorean theorem.
• The diagonal of a rectangle, D =√ (Length)² +(Breadth)²
• Substituting values we get, D =√ {(8)² +(6)² }=√ {(64)+(36)} = $\surd \; \{100$} = 10 meters

Total distance covered by Tom:

• • Total distance = Perimeter + Diagonal = $28+10=38$ meters

Therefore, Tom’s total distance covered is 38 meters.

So, the correct answer is (A) 38 meters.