IS IT POSSIBLE TO HAVE A TRIANGLE WITH SIDES:-

1. 5cm, 7cm and 9cm
2. 8cm, 6cm and 15cm

For any triangle the sum of the length of two sides are always greater than the length of the third side.
Considering (i) we have;
$$\begin{gathered} 5 \mathrm{cm} + 7 \mathrm{cm} = 12 \mathrm{cm}>9 \mathrm{cm} \\ 5 \mathrm{cm} + 9 \mathrm{cm} = 14 \mathrm{cm}> 7\mathrm{cm} \\ 9 \mathrm{cm} + 7 \mathrm{cm} = 16 \mathrm{cm}>5 \mathrm{cm} \end{gathered}$$
Therefore it is possible to have a triangle with sides 5 cm, 7 cm and 9 cm.
Considering (ii) we have;
$$\begin{gathered} 6 \mathrm{cm} + 15 \mathrm{cm} = 21 \mathrm{cm}>8 \mathrm{cm} \\ 8 \mathrm{cm} + 15 \mathrm{cm} = 23 \mathrm{cm}> 6\mathrm{cm} \\ \mathrm{but}; 8 \mathrm{cm} + 6 \mathrm{cm} = 14 \mathrm{cm} \mathrm{which} \mathrm{is} < 15 \mathrm{cm}. \end{gathered}$$
Therefore it is not possible to have a triangle with sides 8 cm, 6 cm and 15 cm.