A took 15 sec to cross a rectangular field diagonally walking at the rate of speed 52 m/min and B took the same time to cross the same field along its sides walking at the rate speed 68 m/min. The area of the field is:

Answer: Option D

Solution

Answer: Option D

Solution:

BD = length of diagonal = speed × time
$$\begin{array}{rl}& =\frac{52}{60}\times 15\\ & =13\text{ m}\\ & \text{BD}=\sqrt{l^2+b^2}\\ & \Rightarrow l^2+b^2=13^2\\ & \Rightarrow l^2+b^2=169\\ & \text{Again, }l+b=\frac{68}{60}\times 15=17\\ & {\left(l+b\right)}^2=l^2+b^2+2lb\\ & 17^2=169+2lb\\ & lb=\frac{120}{2}=60{\text{m}}^2\end{array}$$