Question
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. If the area of the lawn is 2019 then the width of the road isSolution
The length of the park is 60 m The breadth of the park is 40 m The area of the lawn is 2019 m we know that, Area of a Rectangle = length × breadth Let the width of the park is x m The area of the park is ⇒ 60 × 40 = 2400 m2 The area of the road is ⇒ 60 × x + 40 × x - x2 = 2400 - 2019 ⇒ 60x + 40x - x2 = 381 ⇒ x2 - 100x + 381 = 0 ⇒ x2 - 97x - 3x + 381 = 0 ⇒ x(x - 97) - 3(x - 97) = 0 ⇒ (x - 3)(x - 97) = 0 ⇒ x = 3, 97 Since the width of the road cannot be larger than the length and the breadth ∴ The width of the road is 3 metre.
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