Discussion
'P' took 15 seconds to cross a rectangular field diagonally walking at the rate of 56 m/min and 'R' took the same time to cross the same field along its sides walking at the rate of 72 m/min. The area of the field is :
Answer: D
The area is 64 \(\mathrm{m}^{2}\).
In 15 seconds, a quarter of a minute, P covers \(56 \div 4 = 14\) m along the diagonal, and R covers \(72 \div 4 = 18\) m along two sides. With sides l and b:
\[ \begin{aligned} l + b &= 18,\quad l^{2} + b^{2} = 196 \\ 2lb &= (l + b)^{2} - (l^{2} + b^{2}) \\ &= 324 - 196 = 128 \\ lb &= 64 \end{aligned} \]
128 is twice the area, the value of 2lb before dividing by 2.
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