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Given 5 sticks of length 1, 3, 5, 9, and 10, how many distinct triangles can be formed? Learn the techniques and develop an intuition for working with geometric inequalities.

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**largest possible** length for the third side?

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The three side lengths of a non-degenerate triangle are \(x, x + 5\) and \(x + 11.\) Which of the following is NOT a possible value for \(x?\)

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Two of the legs of an isosceles triangle have length 12 and 27 respectively. What is the perimeter of the triangle?

**Details and assumptions**

An isosceles triangle is a triangle with exactly two equal sides.

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