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 m². Find the width of the path.Solution
ATQ, Let width of path = x m Inner rectangle = (50 − 2x) by (40 − 2x) Total area = 2000 m² Area of path = 2000 − (50 − 2x)(40 − 2x) = 344 (50 − 2x)(40 − 2x) = 2000 − 344 = 1656 Expand: (as earlier) (50 − 2x)(40 − 2x) = 2000 − 100x − 80x + 4x² = 4x² − 180x + 2000 So: 4x² − 180x + 2000 = 1656 4x² − 180x + 344 = 0 Divide by 4: x² − 45x + 86 = 0 Check x = 2: 4 − 90 + 86 = 0 ⇒ x = 2 is a root. So width of path = 2 m.
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