The length and breadth of a room are 15 m and 20 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?

1. A

   95 m

2. B

   70 m

3. C

   90 m

4. D

   75 m

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

• The total distance is the sum of the perimeter and the diagonal of the rectangular room.
• First, calculate the perimeter: 2 * (Length + Breadth) = 2 * (15m + 20m) = 70m.
• Next, calculate the diagonal using the Pythagorean theorem: √(Length² + Breadth²) = √(15² + 20²) = √(225 + 400) = √625 = 25m.
• Finally, add the perimeter and the diagonal to find the total distance: 70m + 25m = 95m.

Why Other Options Were Wrong

• Option B: This value represents only the perimeter of the room (the distance along the four walls).
• Option C: This is a calculation error. It does not correspond to the perimeter, the diagonal, or their sum.
• Option D: This is a calculation error. It does not correspond to the perimeter, the diagonal, or their sum.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of geometric formulas for perimeter and diagonal of a rectangle as background academic context rather than a clinical decision trigger.
• While not a clinical question, numeracy and problem-solving are essential skills for nurses, tested in many nursing entrance exams.
• These skills are applied daily in tasks like calculating medication dosages, IV drip rates, and interpreting patient data charts.
• What if the cat ran along the length, breadth, and then the diagonal? The distance would be 15m + 20m + 25m = 60m. Understanding the exact path described in a problem is crucial.

How to Approach the Question

• First, carefully read the question to identify all parts of the path the cat takes. Note that it's a two-part journey: along the walls and then along a diagonal.
• Break the problem down into smaller, manageable steps: 1) Calculate the perimeter, 2) Calculate the diagonal.
• Recall the formula for the perimeter of a rectangle: P = 2 * (length + breadth).
• Recall the Pythagorean theorem to find the diagonal: d² = l² + b².
• Perform the calculations for each step accurately.
• Finally, sum the results from your steps to get the total distance and match it with the given options.

Concept Tested & Keywords

• Concept Tested: Application of geometric formulas for perimeter and diagonal of a rectangle.
• Stem keywords: length, breadth, room, diagonal, total distance
• Lead-in keywords: How much

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