A 2 text{ m} broad pathway is to be construct | vedclass

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(D) Let the length and breadth of the rectangular plot be $l$ and $b$ respectively.Given,the area of the plot is $l 	imes b = 96 	ext{ m}^2$.$A$ pat

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Data inadequate

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(D) Let the length and breadth of the rectangular plot be $l$ and $b$ respectively.Given,the area of the plot is $l 	imes b = 96 	ext{ m}^2$.$A$ pathway of width $2 	ext{ m}$ is constructed inside the plot.The dimensions of the inner rectangle (excluding the path) will be $(l - 4)$ and $(b - 4)$ because the path reduces the length and breadth from both sides.The area of the path is calculated as: $	ext{Area of path} = 	ext{Total Area} - 	ext{Inner Area} = lb - (l - 4)(b - 4)$.Substituting $lb = 96$: $	ext{Area of path} = 96 - (lb - 4l - 4b + 16) = 96 - (96 - 4(l + b) + 16) = 4(l + b) - 16$.Since the values of $l$ and $b$ are not individually known,the sum $(l + b)$ cannot be determined from the given area $lb = 96$ alone.Therefore,the area of the path cannot be calculated,and consequently,the total cost of construction cannot be determined.Thus,the data provided is inadequate.

$A$ $2 \text{ m}$ broad pathway is to be constructed around a rectangular plot on the inside. The area of the plot is $96 \text{ m}^2$. The rate of construction is $₹ 50 / \text{ m}^2$. Find the total cost of construction (in $₹$).

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