ChetanaSforum # Question of the Day (28/8/12)

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A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road? 5 m 4 m 2 m 3 m

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A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road? 5 m 4 m 2 m 3 m

Ans: 3m

ans is 3m

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Ans : 3m...........

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Area of the park =60×40=2400=60×40=2400 m2
Given that area of the lawn =2109=2109 m2
∴ Total area of the cross roads =24002109=291=2400−2109=291 m2

Assume that the width of the cross roads =x=x

Then, total area of the cross roads
= Area of road 11 + Area of road 22 - (Common area of the cross roads)
=60x+40xx2=60x+40x−x2

Now, we have
Total area of cross roads =60x+40xx2=60x+40x−x2
But total area of the cross roads =291=291 m2

Hence,
60x+40xx2=291100xx2=291x2100x+291=0(x97)(x3)=0 x=3.

Therefore the width of the road is 3m.