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

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In the discussion about the distance between lines HO and PB in a cuboid, participants clarify that the correct figure is OBPH, not OBFPH. The original poster calculated the distance using the parallelogram formula and arrived at $$\frac{1}{5}\sqrt5$$. Another participant confirmed this answer and suggested that the question may have been misread. The conversation centers on verifying the calculations and ensuring the correct geometric figure is referenced. The focus remains on accurately determining the distance in the specified cuboid configuration.
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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. $$5\sqrt3$$ cm
B. $$5\sqrt2$$ cm
C. $$\sqrt5$$ cm
D. $$\frac{5}{2}\sqrt2$$ cm
E. $$\frac{5}{3}\sqrt3$$ cm

By making use of the parallelogram formula, I got $$\frac{1}{5}\sqrt5$$. Do you guys get the same answer as me or any of the options?
 
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Monoxdifly said:
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. $$5\sqrt3$$ cm
B. $$5\sqrt2$$ cm
C. $$\sqrt5$$ cm
D. $$\frac{5}{2}\sqrt2$$ cm
E. $$\frac{5}{3}\sqrt3$$ cm

By making use of the parallelogram formula, I got $$\frac{1}{5}\sqrt5$$. 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?
 
Sorry, I meant OBPH.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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