(i) No. It is not possible to construct a triangle with lengths of its sides $$5\\ cm, 4\\ cm$$ and $$9\\ cm$$ because the sum of two sides is not greater than the third side i.e. 5+4 is not greater than 9.(ii) Yes. It is possible to construct a triangle with lengths of its sides $$8\\ cm, 7\\ cm$$ and $$4\\ cm$$ because the sum of two sides of a triangle is greater than the third side.(iii) Yes. It is possible to construct a triangle with lengths of its sides $$10\\ cm, 5\\ cm$$ and $$6\\ cm$$ because the sum of two sides of a triangle is greater than the third side.(iv) Yes. It is possible to construct a triangle with lengths of its sides $$2.5\\ cm, 5\\ cm$$ and $$7\\ cm$$ because the sum of two sides of a triangle is greater than the third side.(v) No. It is not possible to construct a triangle with lengths of its sides $$3\\ cm, 4\\ cm$$ and $$8\\ cm$$ because the sum of two sides is not greater than the third side.