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Home » Combine like terms: \(4x^2 + 50x + 150 = 286\). - Get link 4share

Combine like terms: \(4x^2 + 50x + 150 = 286\). - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 = \sqrt{7056} = 84

📌 The area is 84 m². The shortest altitude corresponds to the longest side, which is 15 m. Using $A = \frac{1}{2} \times \text{base} \times \text{height}$:

📌 = \frac{1}{2} \times 15 \times h \Rightarrow h = \frac{84 \times 2}{15} = \frac{168}{15} = 11.2

📌 Thus, the shortest altitude is $\boxed{11.2}$ meters.

📌 Question:** An archaeologist uses ground-penetrating radar to map a circular foundation of an ancient hut. A rectangular structure, 6 m by 8 m, is perfectly inscribed in the circular base. What is the circumference of the circle in meters? Express your answer in terms of $\pi$.

📌 Solution:** Since the rectangle is inscribed in the circle, its diagonal is the diameter of the circle. Using the Pythagorean theorem:

📌 \text{Diagonal} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ m}

📌 Thus, the diameter $d = 10$ m, so the radius $r = 5$ m. The circumference is:

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