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Classification of Triangles Based on Sides

In Δ XYZ, x, ...

Question

In $Δ$ XYZ, x, y and z denote the three sides. Which of the following is incorrect?

x - y > z

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x + z > y

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x - y < z

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x + y > z

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Solution

The correct option is A x - y > z
One of the most important properties of a triangle is that the sum of the lengths of the two sides of the triangle must be greater than that of the third side. If we take the difference of the length of two sides, then this will be lesser than that of the third side. The difference between two sides of a triangle cannot be greater than the third side.

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y + z - x = \frac{x y z}{a^{2}}, z + x - y = \frac{x y z}{b^{2}}, x + y - z = \frac{x y z}{c^{2}} .

x + y + z = 0

\frac{x^{3} + y^{3}}{x y z} = \frac{y^{3} + z^{3}}{x y z} = \frac{x^{3} + z^{3}}{x y z} = a

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x, y, z

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2 s = x + y + z

\frac{s - x}{4} = \frac{s - y}{3} = \frac{s - z}{2}

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\frac{8 π}{3}

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