Is it possible to construct a triangle with lengths of its sides as $9 \, cm$,$7 \, cm$,and $17 \, cm$? Give reason for your answer.
(N/A) No,it is not possible to construct a triangle with side lengths $9 \, cm$,$7 \, cm$,and $17 \, cm$.
According to the triangle inequality theorem,the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Here,the sum of the two smaller sides is:
$9 \, cm + 7 \, cm = 16 \, cm$
Since $16 \, cm < 17 \, cm$,the sum of the two sides is not greater than the third side.
Therefore,a triangle cannot be formed with these side lengths.
According to the triangle inequality theorem,the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Here,the sum of the two smaller sides is:
$9 \, cm + 7 \, cm = 16 \, cm$
Since $16 \, cm < 17 \, cm$,the sum of the two sides is not greater than the third side.
Therefore,a triangle cannot be formed with these side lengths.
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