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
• Pyramid
  Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
• 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
  Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
• 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
• 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.
• 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?
• 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,
• 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.
• Rhumbline
  Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
• Right-angled triangle base
  Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm.
• Diagonals in diamons/rhombus
  Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
• Rhombus MATH
  Construct a rhombus M A T H with diagonal MT=4cm, angle MAT=120°
• Angle of two lines
  There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
• Diagonal
  The rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has an area of 15 cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
• 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.
• 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.