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Home » Thus, the radius of the inscribed circle is \(\boxed3\). - Blask

Thus, the radius of the inscribed circle is \(\boxed3\). - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A = (5\sqrt{2})^2 = 25 \times 2 = 50 \text{ square cm}

📌 Thus, the area of the larger square is \(\boxed{50}\) square cm.

📌 An equilateral triangle has a perimeter of 18 cm. If each side is increased by 2 cm, by how many square centimeters does the area increase?

📌 The side length \(s\) of the original equilateral triangle is:

📌 s = \frac{18}{3} = 6 \text{ cm}

📌 The area \(A_1\) of an equilateral triangle with side \(s\) is:

📌 A_1 = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} \text{ square cm}

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

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