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?

(l + w) (b + w) - l b

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l b - (l - w) (b - w)

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(l + b - w) w

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l b - (l - 2 w) (b - 2)

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Solution

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.

$∴$ Total area of the path
$= l w + b w - w^{2} = (l + b - w) w$

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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?

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?