Distance of lines

Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm

Correct answer:

x =  4.4721 cm

Step-by-step explanation:

$$\begin{gathered} a=3\text{ cm } \\ b=2\text{ cm } \\ c=4\text{ cm } \\ {u}_1=\sqrt{b^2+c^2}=\sqrt{2^2+4^2}=2\sqrt{5}\text{ cm}\doteq 4.4721\text{ cm } \\ {u}_2=\sqrt{a^2+u_1^2}=\sqrt{3^2+4.4721^2}=\sqrt{29}\text{ cm}\doteq 5.3852\text{ cm } \\ x=u_1=4.4721=2\sqrt{5}=4.4721\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• Deviation of the lines
  Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
• Body diagonal
  Find the length of the body diagonal of a cuboid with edges lengths of 16 cm, 7 cm, and 4 cm.
• Cuboid
  Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
• Body diagonal
  Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
• Prism - box
  The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.
• Diagonals of a prism
  The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.
• Cuboid easy
  The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
• Ratio of edges
  The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
• Prism 4 sides
  The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
• Cuboid - volume, diagonals
  The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
• Body diagonal
  Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
• Body diagonal
  Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
• Height of the cuboid
  Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
• Find diagonal
  Find the length of the diagonal of a cuboid with length=20m width=25m height=150m
• Cuboid face diagonals
  The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
• Wall and body diagonals
  The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
• Prism
  Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'