State whether the following statement is true or false:
An open box measuring $12\, cm \times 4\, cm \times 3\, cm$ can hold a bar of $15\, cm$ in length.

(B) The length of the longest rod that can be placed in a rectangular box of dimensions $l \times b \times h$ is given by the space diagonal formula: $d = \sqrt{l^2 + b^2 + h^2}$.
Given dimensions are $l = 12\, cm$,$b = 4\, cm$,and $h = 3\, cm$.
Calculating the diagonal: $d = \sqrt{12^2 + 4^2 + 3^2} = \sqrt{144 + 16 + 9} = \sqrt{169} = 13\, cm$.
The maximum length of a bar that can fit inside the box is $13\, cm$.
Since the bar is $15\, cm$ long and $15\, cm > 13\, cm$,the bar cannot fit in the box.
Therefore,the statement is False.