The construction of a triangle ABC, given that BC = 3 cm is possible when difference of AB and AC is equal to :

3.2 cm

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3.1 cm

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3 cm

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2.8 cm

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Solution

The correct option is B 2.8 cm
Let the length of $A B$ be $x$ and $A C$ be $y$
A triangle can be formed if the sum of any two sides is greater then the third
$\Rightarrow B C + A C > A B \Rightarrow 3 + A C > A B \Rightarrow 3 > A B - A C \Rightarrow A B - A C < 3$
So only option $D$ is correct.

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