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Home » $S_1 = 1$ (string: 3) - Dyverse

$S_1 = 1$ (string: 3) - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 If each side is increased by 2 cm, the new side length is \(8\) cm. The new area \(A_2\) is:

📌 A_2 = \frac{\sqrt{3}}{4} \times 8^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3} \text{ square cm}

📌 A_2 - A_1 = 16\sqrt{3} - 9\sqrt{3} = 7\sqrt{3} \text{ square cm}

📌 Thus, the area increases by \(\boxed{7\sqrt{3}}\) square cm.

📌 A rectangle with dimensions 3 cm by 4 cm is inscribed in a circle. What is the circumference of the circle?

📌 The diagonal of the rectangle is the diameter of the circle. Using the Pythagorean theorem, the diagonal \(d\) is:

📌 d = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm}

📌 The radius \(r\) of the circle is half of the diameter:

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