The construction of a $∆ A B C$ in which $A B = 6 c m$ , $∠ A = 45 °$ is possible when $(B C + A C)$ is

$7 c m$

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$5 c m$

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$5.8 c m$

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$4.9 c m$

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Solution

The correct option is A
$7 c m$

Find the value of $B C + A C$
It is known that the construction of a triangle can only be possible if the sum of two sides is greater than the third side.
It is given that $A B = 6 c m$ .
So, the sum of the other two sides will be greater than $A B$ .
Thus,
$B C + A C > A B$
This condition is only satisfied by option(a).
Hence, the correct option is (a) $7 c m$ .

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