Question

The perimeter of a rectangular plot is 34 m and its area is 60 m². In what time a cat can cross the plot diagonally at a speed of 2.5 m/s?
1. 5.5 seconds
2. 5.2 seconds
3. 5.8 seconds
4. 5.6 seconds

Answer 1

Correct Answer - Option 2 : 5.2 seconds

Given:

Perimeter of plot = 34 m

Area of plot = 60m²

Speed of cat = 2.5 m/s

Concept:

Calculate the length and breadth of the rectangular plot and then the diagonal of the plot. Finally, calculate the time taken by the cat to cross the plot.

Formula Used:

Perimeter of rectangle = 2(l + b)

Area of rectangle = l × b

Diagonal of rectangle = √(l² + b²)

Time taken = Distance/speed

Where,

l → Length of rectangle

b → breadth of rectangle

Calculation:

Area of rectangle = l × b = 60 m²      ----(1)

Perimeter of rectangle = 2(l + b) = 34 m

⇒ l + b = 17 m ----(2)

Take square of both side of eq. (2)

⇒ (l + b)² = 17²

⇒ l² + b² + 2lb = 289

⇒ l² + b² + 2 × 60 = 289

⇒ l² + b² = 289 – 120

⇒ l² + b² = 169

Diagonal of rectangle plot = √(l² + b²)

⇒ √(169) = 13 m

Time taken by cat to cross the field = 13/2.5 = 5.2 seconds.

∴ Time taken by cat to cross the field diagonally is 5.2 seconds