In $\Delta ABC$,$AB = 8 \text{ cm}$ and $BC = 10 \text{ cm}$. Then the perimeter of $\Delta ABC$ is less than how many centimeters?

In $\Delta ABC$,$AB = 6 \, cm$,$BC = 8 \, cm$,and $AC = 10 \, cm$. $BM$ is an altitude on $AC$. Then $BM = \dots \, cm$.

Side $QR$ of $\Delta PQR$ is extended on both the sides so that exterior angles $\angle PQS$ and $\angle PRT$ are formed. If $\angle PQS = 100^{\circ}$ and $\angle PRT = 130^{\circ}$,find the measure of each angle of $\Delta PQR$.

State whether the following statement is true or false:
$(1)$ In $\Delta PQR$,$\angle P = \angle Q = 95^{\circ}$ is possible.

$Q$ is a point on the side $SR$ of a $\triangle PSR$ such that $PQ = PR$. Prove that $PS > PQ$.

State whether the following statement is True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $\angle B = 105^{\circ}, \angle C = 90^{\circ}$ and $AB + BC + AC = 10 \, cm$.