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Home » Subtract the first equation from this: - Londonproperty

Subtract the first equation from this: - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 A rectangular garden measuring 20 meters by 15 meters is surrounded by a uniform path of width \( x \) meters. If the total area including the path is 504 square meters, what is \( x \)?

📌 Total length including path: \( 20 + 2x \), total width: \( 15 + 2x \)

📌 Total area: \( (20 + 2x)(15 + 2x) = 504 \)

📌 Expand: \( 300 + 40x + 30x + 4x^2 = 504 \)

📌 \( 4x^2 + 70x + 300 = 504 \Rightarrow 4x^2 + 70x - 204 = 0 \)

📌 Divide by 2: \( 2x^2 + 35x - 102 = 0 \)

📌 \( x = rac{-35 \pm \sqrt{35^2 - 4(2)(-102)}}{2(2)} \)

📌 \( x = rac{-35 \pm \sqrt{1225 + 816}}{4} = rac{-35 \pm \sqrt{2041}}{4} \)

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