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Question

A rectangular garden has an area 2000m2 and its length and breadth are in the ratio 5 : 4 A road of uniform width runs inside the garden around the perimeter and has an area 344m2 then the width of the road is

A
4 m
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B
3.5 m
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C
3 m
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D
2 m
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Solution

The correct option is D 2 m
The length and width in ratio 5:4 . Let Length is 5x and width is 4x
Then area of rectangle =5x×4x2000020x2=20000x2=100x=10
So length of rectangle =50 m and width=40 m
Let Y m width road inside around permeter
Then area of road in length side =2×50×y=100y m
And area of road in width side=2(402y)y=80y4y2 m
Total area of road=100y+80y4y2m
But area of road is 344 sq m Given
100y+80y4y2=344
$\Rightarrow -4y^{2}+180y=344$
y245y+86=0
y243y2y+86=0
y(y43)2(y43)=0
Then y=2 or y=43
But y=43 is not possiblebecause width is 40 m
Then width of road =2 m

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