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it's always sunny in philadelphia series - AdVision eCommerce

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 For side 14 m: \( h_{14} = \frac{168}{14} = 12 \) m

📌 For side 15 m: \( h_{15} = \frac{168}{15} = 11.2 \) m

📌 The shortest altitude is \( \frac{168}{15} = 11.2 \) m. Thus, the length of the shortest altitude is:

📌 A quantitative researcher models a population distribution using a right triangle where the legs represent two demographic variables. If the hypotenuse is \( z \) and the inradius is \( c \), what is the ratio of the area of the inscribed circle to the area of the triangle?

📌 The area \( A \) of a right triangle with legs \( a \) and \( b \) is:

📌 A = \frac{1}{2}ab.

📌 The inradius \( c \) of a right triangle is given by:

📌 where \( z = \sqrt{a^2 + b^2} \). Also, the area can express in terms of the inradius:

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