A rectangular park 60 m long and 40 m wide has two concrete crossroads running through the middle of the park, and the rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

2.91 m
3 m
5.82 m
None of these

Correct answer: 3 m

Solution

Total area of the park is $60 \times 40 = 2400$ sq. m. Since lawn area is 2109 sq. m, road area is $2400 - 2109 = 291$ sq. m. For two perpendicular roads of width $x$, road area is $60x + 40x - x^2 = 100x - x^2$, and solving gives $x=3$ m.

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