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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×4x20000⇒20x2=20000⇒x2=100⇒x=10So length of rectangle =50 m and width=40 mLet Y m width road inside around permeterThen area of road in length side =2×50×y=100y mAnd area of road in width side=2(40−2y)y=80y−4y2 mTotal area of road=100y+80y−4y2mBut area of road is 344 sq m Given∴100y+80y−4y2=344$\Rightarrow -4y^{2}+180y=344$⇒y2−45y+86=0⇒y2−43y−2y+86=0⇒y(y−43)−2(y−43)=0Then y=2 or y=43But y=43 is not possiblebecause width is 40 mThen width of road =2 m

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