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Home » A rectangle's diagonal is 10 cm, and one side is 6 cm. What is the area of the rectangle? - AMAZONAWS

A rectangle's diagonal is 10 cm, and one side is 6 cm. What is the area of the rectangle? - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 A rectangular garden measures 15 meters in length and 10 meters in width. A path of uniform width is to be built around the garden, increasing the total area to 231 square meters. What is the width of the path?

📌 Let the width of the path be \( x \) meters. The new dimensions of the garden including the path will be \( (15 + 2x) \) meters by \( (10 + 2x) \) meters. The total area is given by:

📌 Expanding the equation:

📌 + 30x + 20x + 4x^2 = 231

📌 4x^2 + 50x + 150 = 231

📌 4x^2 + 50x - 81 = 0

📌 Solving this quadratic equation using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 4 \), \( b = 50 \), and \( c = -81 \):

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