Question 49

Suresh took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min, and Rajesh took the same time to cross the same field along its sides walking at the rate of 68m/min. Find the area of the field.

Solution

Distance travelled by Suresh in 15 sec = $$ \frac{52 \times 15}{60} = 13 m $$

Therefore, diagonal of the field = 13 m

$$ l^2 + b^2 = 13^2 = 169 $$

Distance travelled by Rajesh in 15 sec = $$ \frac{68 \times 15}{60} = 17 m $$

l + b = 17 m

$$ (l + b)^2 = l^2 + b^2 + 2lb $$

289 = 169 + 2lb

120 = 2lb

lb = $$ 60 m^2 $$

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