Question : The length and breadth of a rectangular field in the ratio of $7:4$. A path $4\operatorname{ m }$ wide running all around outside has an area of $416\operatorname{ m^2 }$. The breadth (in $\operatorname{m }$) of the field is:
Option 1: 28
Option 2: 14
Option 3: 15
Option 4: 16
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Correct Answer: 16
Solution :
If a path of $x$ m wide runs around a rectangular field having $l$ as the length and $b$ as the breadth then,
Area of path = $2x(l+b+2x)$
We have the length and breadth of a rectangular field in the ratio of $7:4$. A path $4\operatorname{ m }$ wide running all around outside has an area of $416\operatorname{ m^2 }$.
Let the length and breadth of a rectangular field be $7y$ and $4y$.
Area of the path = $2×4(7y+4y+2×4)$
$⇒416=8(7y+4y+8)$
$⇒11y=44$
$⇒y=4$
So, the breadth of the rectangular field $= 4y=16\operatorname{ m}$
Hence, the correct answer is 16.
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