If a = b + c, then is it true that |a| = |b|+|c|? Justify your answer.

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Solution

In triangle ABC, let CB = a, CA = b and AB = c (as shown in the following figure)
Now, by the triangle law of addition, we have a = b + c.
It is clearly known that |a|; |b| and |c| represent the side of $△$ ABC.
Also, it is known that the sum of the lengths of any two sides of a triangle is greater than the third side.
$∴ | a | < | b | + | c |$
Hence, it is not true that |a| = |b| + |c|.

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