Triangle Inequality Property

Is it possible to have a triangle with the following sides?

$10.2 \mathrm{cm}, 5.8 \mathrm{cm}, 4.5 \mathrm{cm}$

Is it possible to have a triangle with the following sides?

 $3 \mathrm{cm}, 6 \mathrm{cm}, 7 \mathrm{cm}$

Is it possible to have a triangle with the following sides?

 $6 \mathrm{c}\mathrm{m},3 \mathrm{c}\mathrm{m},2 \mathrm{c}\mathrm{m}$

Calculate the angles of a triangle $\mathrm{ABC}$ having $3\angle \mathrm{B}=4\angle \mathrm{C}$ and the interior $\angle \mathrm{A}=\frac{3}{7}$ of exterior $\angle \mathrm{A}$.

$\mathrm{AM}$ is median of $∆\mathrm{ABC}$. Prove that $\mathrm{AB}+\mathrm{BC}+\mathrm{CA}>2\mathrm{AM}$

In the given figure, $S$ is a point on the side $QR$ of $∆PQR$, Prove that $PQ+QR+PR>2PS$.

The lengths of two sides of a triangle are $6 \mathrm{cm} \text{and} 8 \mathrm{cm}$. Between which two numbers can the length of the third side fall?