The owner of a property intends to place a support rod to better secure two posts of equal lengths of 6 m and 4 m. The figure represents the real situation in which the posts are described by segments $AC$ and $BD$ and the rod is represented by segment $EF$, all perpendicular to the ground, which is indicated by the line segment $AB$. The segments $AD$ and $BC$ represent steel cables that will be installed. What should be the value of the length of the rod $EF$? (A) 1 m (B) 2 m (C) $2.4 \text{ m}$ (D) 3 m (E) $2\sqrt{6} \text{ m}$
The owner of a property intends to place a support rod to better secure two posts of equal lengths of 6 m and 4 m. The figure represents the real situation in which the posts are described by segments $AC$ and $BD$ and the rod is represented by segment $EF$, all perpendicular to the ground, which is indicated by the line segment $AB$. The segments $AD$ and $BC$ represent steel cables that will be installed.
What should be the value of the length of the rod $EF$?
(A) 1 m
(B) 2 m
(C) $2.4 \text{ m}$
(D) 3 m
(E) $2\sqrt{6} \text{ m}$