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what is -12 as a rational number - AdVision eCommerce

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 $$Question: A triangle has side lengths of $13$, $14$, and $15$ units. What is the length of the shortest altitude drawn to the longest side?

📌 Solution: The longest side of the triangle is $15$, and the altitude drawn to this side corresponds to the smallest altitude if the area is fixed. First, compute the area using Herons formula. The semi-perimeter is:

📌 The altitude $h$ corresponding to the side of length $15$ is given by:

📌 Solution: The original triangle has side lengths $10$, $24$, $26$. First, verify it is a right triangle:

📌 So, it is a right triangle. The area is:

📌 Since the triangle remains similar, the area scales with the square of the scaling factor $k$. So:

📌 The inradius $c$ of a right triangle is given by:

📌 We now express $ab$ in terms of $z$ and $c$. From the inradius formula:

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