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Home » a_n = \fracn^2 + 1n + 1 - DNSFLEX

a_n = \fracn^2 + 1n + 1 - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 + \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{\sqrt{3}} + \frac{1}{\sqrt{3}} = \frac{\sqrt{3} + 1}{\sqrt{3}}

📌 To rationalize the denominator, multiply the numerator and denominator by \(\sqrt{3}\):

📌 \frac{\sqrt{3} + 1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}(\sqrt{3} + 1)}{3} = \frac{3 + \sqrt{3}}{3}

📌 \boxed{\frac{3 + \sqrt{3}}{3}}

📌 Question:** In a triangle with side lengths 7, 24, and 25 units, find the length of the shortest altitude.

📌 The triangle with sides 7, 24, and 25 is a right triangle because \(7^2 + 24^2 = 49 + 576 = 625 = 25^2\).

📌 The area \(A\) of the triangle can be calculated using the two shorter sides, 7 and 24, as the base and height:

📌 A = \frac{1}{2} \times 7 \times 24 = 84

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