Question

The length and breadth of a rectangular plot are $l$ and $b$ units respectively. Two rectangular paths each of width $w$ units run inside the plot one parallel to the length and the other parallel to the breadth. What is the total area (in sq. units) of the paths?

• A. $(l+w)(b+w)-lb$
• B. $lb-(l-w)(b-w)$
• C. $(l+b-w)w$
• D. $lb-(l-2w)(b-2)$

Answer 1

The correct option is C $(l+b-w)w$


Area of the path along length = $l\times w$
Area of the path along breadth =$b\times w$
The common area of the paths which was counted twice = $w^2$

We need to subtract this area from the sum of the areas of the path along the length and breadth of the plot.

$\therefore$ Total area of the path
$=lw+bw-w^2=(l+b-w)w$