question_answer

The length and breadth of a rectangular plot are I and b. Two rectangular paths each of width W 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)  \[(l+w)\,(b+w)-lb\]

B)   \[l\,b-(l-w)\,(b-w)\]

C)  \[(l+b-w)w\]  

D)  \[l\,b-(l-2w)\,(b-2w)\]

Correct Answer: C

Solution :

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