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lego dimensions lego dimensions - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 D) False — area is $ \frac{1}{2}ab $, and $ r s = r \cdot \frac{a+b+c}{2} $, and $ r = \frac{a+b-c}{2} $, so $ r s = \frac{a+b-c}{2} \cdot \frac{a+b+c}{2} = \frac{(a+b)^2 - c^2}{4} = \frac{a^2 + 2ab + b^2 - c^2}{4} $. Since $ c^2 = a^2 + b^2 $, this becomes $ \frac{2ab}{4} = \frac{ab}{2} $ — yes.

📌 E) $ r s = \frac{ab}{2} $ — true

📌 But best choice:

📌 D) False — although $ r s = \frac{ab}{2} $, the statement area equals $ r \cdot s $ is analytically true only when $ r $ is inradius, which it is — so D is misleading.

📌 C) False — the identity $ A = r s $ is valid only if $ r $ is the inradius, which it is, so C is incorrect.

📌 Wait: $ A = r s $ is always true for inradius $ r $. So area is $ r s $ by definition when $ r $ is inradius.

📌 So the statement the area of the circle over the area of the triangle depends, but here: the area of the triangle is $ r \times s $ — yes, this is correct.

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