The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of $\mathbf{6}$ and $\mathbf{12}$, which inequality represents the possible lengths, $\bm{x}$, of the third side of the triangle?

MM

Mashaal Masha

Apr 11, 2024

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of $\mathbf{6}$ and $12$, which inequality represents the possible lengths, $x$, of the third side of the triangle?

Difficulty: Hard

A:

$x<18$

B:

$x>18$

C:

$6<x<18$

D:

$x<6$ or $x>18$

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