What Is the Distance Between Lines HO and PB in a Cuboid?

[Monoxdifly]

In an ABCD.EFGH cuboid with AB = 4 cm, BC = 3 cm, and CG = 5 cm there is a parallelogram OBFPH with O is located at the center of ABCD and P is located at the center of EFGH. The distance between the lines HO and PB is ...
A. \(\displaystyle 5\sqrt3\) cm
B. \(\displaystyle 5\sqrt2\) cm
C. \(\displaystyle \sqrt5\) cm
D. \(\displaystyle \frac{5}{2}\sqrt2\) cm
E. \(\displaystyle \frac{5}{3}\sqrt3\) cm

By making use of the parallelogram formula, I got \(\displaystyle \frac{1}{5}\sqrt5\). Do you guys get the same answer as me or any of the options?

 

[Opalg]

In an ABCD.EFGH cuboid with AB = 4 cm, BC = 3 cm, and CG = 5 cm there is a parallelogram OBFPH with O is located at the center of ABCD and P is located at the center of EFGH. The distance between the lines HO and PB is ...
A. \(\displaystyle 5\sqrt3\) cm
B. \(\displaystyle 5\sqrt2\) cm
C. \(\displaystyle \sqrt5\) cm
D. \(\displaystyle \frac{5}{2}\sqrt2\) cm
E. \(\displaystyle \frac{5}{3}\sqrt3\) cm

By making use of the parallelogram formula, I got \(\displaystyle \frac{1}{5}\sqrt5\). Do you guys get the same answer as me or any of the options?

OBFPH is not a parallelogram. Did you mean OBPH? If so, then I agree with your answer $\frac15\sqrt5$. But maybe you misread the question?

 

[Monoxdifly]

Sorry, I meant OBPH.