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Home » \[ 3y = rac697 \] - jntua results

\[ 3y = rac697 \] - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \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

📌 The altitude corresponding to the hypotenuse (side of length 25) is the shortest because the height is smallest when based on the longest side. Let \(h\) be the altitude to the hypotenuse. The area can also be written as:

📌 A = \frac{1}{2} \times 25 \times h

📌 Equating the two expressions for area:

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