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Home » Now solve the first and new second equation: - Decision Point

Now solve the first and new second equation: - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 However, in a right triangle, its known that $ a + b - c = 2r $, so solving for $ r $ gives:

📌 Question: A seismologist models the fault line between two tectonic plates as a triangle with side lengths $ 13 $ km, $ 14 $ km, and $ 15 $ km. Find the length of the shortest altitude in the triangle.

📌 Solution: To find the shortest altitude, we first compute the area of the triangle using Herons formula. The semiperimeter $ s $ is:

📌 Question: A science communicator explains geometric scaling using a triangle with side lengths $ 3 $, $ 4 $, and $ 5 $. If each side is scaled by $ k $, and the inradius of the scaled triangle is $ 6 $, find the value of $ k $.

📌 Solution: The original triangle is a right triangle with area:

📌 Question: A seismologist analyzes a triangular fault zone with sides $ 7 $, $ 24 $, and $ 25 $. Find the radius of the inscribed circle, representing the zones effective monsoon drainage radius.

📌 Question: What is the remainder when $11071 + 11073 + 11075 + 11077 + 11079$ is divided by 17?

📌 Question: What is the smallest three-digit number divisible by both 19 and 29, representing the optimal number of satellite sensors for a glacier monitoring system?

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