The construction of $Δ A B C,$ given that $B C = 3 c m$ , is possible when the difference of the sides $A B$ and $A C$ is equal to

3.2 c m

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3.1 c m

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3 c m

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2.8 c m

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Solution

The correct option is D $2.8 c m$
The construction of a triangle is possible if the sum of two sides is greater than the third side, i.e.,
$A B + B C > A C$
$\Rightarrow B C > A C - A B$
$\Rightarrow 3 c m > A C - A B$

So, if $A C - A B = 2.8 c m$ , then the construction of $Δ A B C$ with the given conditions is possible.

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