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Can a scalene triangle be obtuse? Is an equilateral triangle always acute?

If the above triangle is an equilateral triangle and the length of \(\overline{AB}\) is \( \lvert \overline {AB} \rvert =11 ,\) what is \( \lvert \overline {AC} \rvert ?\)

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If \( \triangle ABC \) is a right triangle and the lengths of two sides are \( \lvert \overline {AB} \rvert = 6\) and \(\lvert \overline {AC} \rvert = 8 ,\) what is \( \lvert \overline {BC} \rvert ?\)

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\( \triangle {ABC} \) is an acute triangle with side lengths \( \lvert \overline {AB} \rvert = 120\) and \(\lvert \overline {AC} \rvert = 160.\) If \(\lvert \overline {BC} \rvert \geq \lvert \overline {AC} \rvert, \) what is the possible range of \( \lvert \overline {BC}\rvert?\)

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Solid figure \(ABCDEFGH\) is a regular cube with side length \( 12.\) What is the area of \( \triangle DEF ?\)

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Angle \(\angle A\) is an obtuse angle in triangle \(ABC\) with side lengths \( \lvert \overline {AB} \rvert = 30\) and \(\lvert \overline {AC} \rvert = 40.\) If \(\lvert \overline {BC} \rvert\) is an integer and \(\lvert \overline {BC} \rvert \geq \lvert \overline {AC} \rvert, \) what is the minimum value of \(\lvert \overline {BC}\rvert ?\)

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