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Home » The Secret Step to Draw a Perfect Heart in Seconds—Watch Now! - Abbey Badges

The Secret Step to Draw a Perfect Heart in Seconds—Watch Now! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Equality holds when \( \frac{x}{y} = \frac{y}{z} = \frac{z}{x} \), which implies \( x = y = z \). Given \( x + y + z = 3 \), we get \( x = y = z = 1 \). Substituting:

📌 \frac{1^2}{1} + \frac{1^2}{1} + \frac{1^2}{1} = 1 + 1 + 1 = 3

📌 Thus, the minimum value is \( \boxed{3} \).Question:

📌 A linguist studying the evolution of sign language observes that a triangular gesture board has sides of lengths 13 cm, 14 cm, and 15 cm. Compute the area of the triangle and use it to find the radius of the inscribed circle.

📌 To find the area of the triangle with sides \(a = 13\), \(b = 14\), and \(c = 15\), we use Heron's formula. The semi-perimeter \(s\) is:

📌 The area \(A\) is given by:

📌 A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21(21-13)(21-14)(21-15)}

📌 A = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056} = 84

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