Question

A walks along the diagonal of a rectangle with 52 m/min speed in 15 sec and B walks along the side of the rectangle with 68 m/min speed and reach the same point at the same time. Find the area of the rectangle ?  
1. 50 m²
2. 80 m²
3. 60 m²
4. 120 m²

Answer 1

Correct Answer - Option 3 : 60 m²

Given - 

speed of A = 52 m/min

speed of B = 68 m/min

time = 15 sec

Formula used - 

speed = distance/time

1 hour = 60 min

1 min = 60 sec

If a rectangle having length l and breadth b

diagonal = √(l² + b²)

area = l × b

(a + b)² = a² + 2ab + b²

Solution - 

Let the length and breadth of the rectangle be l and b.

According to question - 

⇒ {√(l² + b²)/(52/60)} = 15

⇒ √(l² + b²) = 13

⇒ (l² + b²) = 169 .......................................(1)

⇒ Again, for B

⇒ {(l + b)/(68/60)} = 15

⇒ (l + b) = 17

⇒ Squaring both sides - 

⇒ l² + b² + 2lb = 289

⇒ 2lb = 289 - 169              (from equation (1))

⇒ lb = 60 m²

∴ area of rectangle is 60 m².