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# Geometric Inequalities

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.

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

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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