Question

A rectangular garden has an area $2000m^2$ 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 $344m^2$ then the width of the road is

• A. 4 m
• B. 3.5 m
• C. 3 m
• D. 2 m

Answer 1

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 =$\therefore 5x\times 4x20000\Rightarrow 20x^2=20000\Rightarrow x^2=100\Rightarrow x=10$

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 =$2\times 50\times y=100y$ m

And area of road in width side=$2(40-2y)y=80y-4y^2$ m

Total area of road=$100y+80y-4y^2$m

But area of road is 344 sq m Given

$\therefore 100y+80y-4y^2=344$

$\Rightarrow -4y^{2}+180y=344$

$\Rightarrow y^2-45y+86=0$

$\Rightarrow y^2-43y-2y+86=0$

$\Rightarrow y(y-43)-2(y-43)=0$

Then y=2 or y=43

But y=43 is not possiblebecause width is 40 m

Then width of road =2 m