question_answer

The length and breadth of a rectangular plot are \[1\] and\[b\]. Two rectangular paths each of width 'r' run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area of the paths?

A)  \[(1+r)(b+r)-1b\]

B)  \[1b-(1-r)(b-r)\]

C)  \[(1+b-r)r\]

D)  \[1b-(1-2r)(b-2r)\]

Correct Answer: C

Solution :

Area of the path along length \[=l\times r\] Area of the path along breadth \[=b\times r\] The common area of the paths \[={{b}^{2}}\] \[\therefore \]Total area of the path \[=lr+lr-{{r}^{2}}=(l+b-r)r\]