A rectangular farm house has a `1km` difference between its sides. Two farmers simultaneously leave one of the vertex of the rectangle for a point at the opposite vertex. One farmer crosses the farmhouse along its diagonal and other walks along the edge. The speed of each farmer is `4km//hr`. If one of them arrives half an hour earlier then the other then the size of farmhouse is .

Options

A. `12kmxx13km`
B. `4kmxx5km`
C. `3kmxx4km`
D. None of these

Answer

C

Explanation

According to given condition
`(d+1+d)/(4)=sqrt((d+1)^(2)+d^(2))/(4)=(1)/(2)`
`rArr2d1=sqrt((d^(2)+(d+1)))gtd=3km`
`rArr` size of farm house `3kmxx4km`