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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A rectangular garden is 30 meters long and 20 meters wide. A path of uniform width surrounds the garden. If the total area of the garden and the path is 936 square meters, what is the width of the path?

📌 Let \( x \) be the width of the path.

📌 The dimensions including the path are \( (30 + 2x) \) meters by \( (20 + 2x) \) meters.

📌 The total area equation is \( (30 + 2x)(20 + 2x) = 936 \).

📌 Expanding: \( 600 + 60x + 40x + 4x^2 = 936 \).

📌 Simplifying: \( 4x^2 + 100x + 600 = 936 \).

📌 Subtract 936 from both sides: \( 4x^2 + 100x - 336 = 0 \).

📌 Divide the entire equation by 4: \( x^2 + 25x - 84 = 0 \).

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