[ASK] Parallelogram in Cuboid

Yes, I agree with your answer of $\frac15\sqrt5$. The options do not match the correct answer. In summary, the distance between the lines HO and PB in a cuboid with given dimensions is $\frac15\sqrt5 cm$.
  • #1
Monoxdifly
MHB
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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. \(\displaystyle 5\sqrt3\) 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?
 
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  • #2
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. \(\displaystyle 5\sqrt3\) 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?
 
  • #3
Sorry, I meant OBPH.
 

What is a parallelogram in a cuboid?

A parallelogram in a cuboid is a two-dimensional shape that is formed by the intersection of two adjacent faces of a three-dimensional cuboid. It is a quadrilateral with two pairs of parallel sides.

How is a parallelogram different from a rectangle in a cuboid?

A rectangle is a special type of parallelogram where all four angles are right angles. In a cuboid, a rectangle can be formed by the intersection of two pairs of adjacent faces, while a parallelogram can be formed by the intersection of any two adjacent faces.

What are the properties of a parallelogram in a cuboid?

In a cuboid, a parallelogram has two pairs of parallel sides and two pairs of equal opposite angles. The opposite sides are also equal in length.

How can a parallelogram be used in a cuboid?

A parallelogram in a cuboid can be used to find the area and perimeter of the cuboid. It can also be used to determine the diagonal length of the cuboid or to calculate the volume of a portion of the cuboid.

Can a parallelogram exist in other three-dimensional shapes?

Yes, a parallelogram can exist in other three-dimensional shapes such as a prism or a pyramid. In these shapes, the parallelogram is formed by the intersection of two adjacent faces.

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