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 $AB + BC + AC = 10 \, cm$.

(B) The given statement is False.
In any triangle $ABC$,the sum of all interior angles must be equal to $180^{\circ}$,i.e.,$\angle A + \angle B + \angle C = 180^{\circ}$.
Given that $\angle B = 105^{\circ}$ and $\angle C = 90^{\circ}$.
Calculating the sum of the two given angles: $\angle B + \angle C = 105^{\circ} + 90^{\circ} = 195^{\circ}$.
Since $195^{\circ} > 180^{\circ}$,the sum of two angles alone exceeds the angle sum property of a triangle. Therefore,such a triangle cannot be constructed.