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$ a_2 = 3 $ - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Un jardin rectangulaire mesure 15 mètres de long et 10 mètres de large. Un chemin de largeur uniforme est construit autour du jardin, augmentant la superficie totale à 264 mètres carrés. Quelle est la largeur du chemin ?

📌 Soit \( x \) la largeur du chemin.

📌 Les nouvelles dimensions sont \( (15 + 2x) \) par \( (10 + 2x) \).

📌 L'équation est \( (15 + 2x)(10 + 2x) = 264 \).

📌 Développez : \( 150 + 30x + 20x + 4x^2 = 264 \).

📌 Simplifiez : \( 4x^2 + 50x - 114 = 0 \).

📌 Résolvez en utilisant la formule quadratique : \( x = \frac{-50 \pm \sqrt{50^2 - 4 \times 4 \times (-114)}}{2 \times 4} \).

📌 Calculez : \( x = \frac{-50 \pm \sqrt{2500 + 1824}}{8} = \frac{-50 \pm \sqrt{4324}}{8} \).

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