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    Question

    A rectangular park is 50 m long and 40 m wide. A path of

    uniform width is built inside the park along the boundary. The area of the path is 344 mΒ². Find the width of the path.
    A 2 m Correct Answer Incorrect Answer
    B 5 m Correct Answer Incorrect Answer
    C 10 m Correct Answer Incorrect Answer
    D 18 m Correct Answer Incorrect Answer

    Solution

    ATQ, Let width of path = x m Inner rectangle = (50 βˆ’ 2x) by (40 βˆ’ 2x) Total area = 2000 mΒ² Area of path = 2000 βˆ’ (50 βˆ’ 2x)(40 βˆ’ 2x) = 344 (50 βˆ’ 2x)(40 βˆ’ 2x) = 2000 βˆ’ 344 = 1656 Expand: (as earlier) (50 βˆ’ 2x)(40 βˆ’ 2x) = 2000 βˆ’ 100x βˆ’ 80x + 4xΒ² = 4xΒ² βˆ’ 180x + 2000 So: 4xΒ² βˆ’ 180x + 2000 = 1656 4xΒ² βˆ’ 180x + 344 = 0 Divide by 4: xΒ² βˆ’ 45x + 86 = 0 Check x = 2: 4 βˆ’ 90 + 86 = 0 β‡’ x = 2 is a root. So width of path = 2 m.

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