Question

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

• A. 30 m²
• B. 40 m²
• C. 50 m²
• D. 60 m²
• E. 69 m²

Answer 1

The correct option is D

60 m²

Length of diagonal = $\left(52\times \frac{15}{60}\right)m=13m.$ Sum of length and breadth = $\left(68\times \frac{15}{60}\right)m=17m$ $\therefore$$\sqrt{l^2+b^2}=13or{l}^2+b^2=169$and l + b = 17 Area = lb =$\frac{1}{2}\left(2lb\right)=\left[\right(l+b){]}^2-(l^2+b^2)]=\frac{1}{2}[(17{)}^2-169]=\frac{1}{2}(289-169)=60m^2$