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Classification of Triangles

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

Classification by Sides

         

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

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 \( \lvert \overline {BC} \rvert ?\)

\( \triangle {ABC} \) 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 \( \lvert \overline {BC}\rvert?\)

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

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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