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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.

Triangle Inequality

The side lengths of a non-degenerate $$\triangle ABC$$ are $$4, 11$$ and $$c.$$ Which of the following is a possible value for $$c?$$

Two legs of a triangle have lengths of 7.4 and 17.3 respectively. Given that the length of the third side is a whole number, what is the largest possible length for the third side?

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 $$x?$$

Three positive integers $$a, b$$ and $$c$$ are the side lengths of $$\triangle ABC.$$ If $$c$$ is the longest side and $$a + b + c = 21,$$ what is the maximum value of $$c?$$

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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