The ratio of the lengths of the three line segments is $1 : 2 : 3$ . If the sum of their lengths is $12 c m$ , can these three line segments form a triangle?

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Solution

Let the segments be $x, 2 x, 3 x$
$x + 2 x + 3 x = 12$
$6 x = 12$
$x = 2$
$2, 4, 6$
According to triangle in equality
sum of there sides > third sides
$2 + 4 = 6 > 6$ false
$∴$ triangle cannot be formed.

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