A boy can diagonally cross a square field of area 98 m2 in 28 seconds. In how much time will he diagonally cross a rectangular field of area 168 m2 and perimeter of 62 m walking at the same speed?

A boy can diagonally cross a square field of area 98 m2 in 28 seconds. In how much time will he diagonally cross a rectangular field of area 168 m2 and perimeter of 62 m walking at the same speed? Correct Answer 50 sec.

Area of square = (side)² and Diagonal of square = √2 × side

⇒ Side of square field = √98 = 7√2 m

Hence, diagonal of square field = √2 × 7√2 = 14 m

⇒ Speed of boy = Diagonal of square field/Time taken = 14/28 = 0.5 m/sec.

Now,

Let the length and breadth of rectangular field be ‘l’ m and ‘b’ m respectively

⇒ Area of rectangular field = lb = 168 m²

⇒ Perimeter of rectangular field = 2(l + b) = 62

⇒ l + b = 31

Substituting for b,

⇒ l + 168/l = 31

⇒ l² – 31l + 168 = 0

⇒ (l – 24)(l – 7) = 0

⇒ l = 24, 7

Hence, b = 7, 24

⇒ Diagonal of rectangular field = √(l² + b²) = √(576 + 49) = √625 = 25 m