Distance of lines

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

Correct result:

x =  4.472 cm

Solution:

a=3 cm b=2 cm c=4 cm  u1=b2+c2=22+42≐2 5 cm≐4.4721 cm u2=a2+u12=32+4.47212≐29 cm≐5.3852 cm  x=u1=4.4721=2 5=4.472 cma=3 \ \text{cm} \ \\ b=2 \ \text{cm} \ \\ c=4 \ \text{cm} \ \\ \ \\ u_{1}=\sqrt{ b^2+c^2 }=\sqrt{ 2^2+4^2 } \doteq 2 \ \sqrt{ 5 } \ \text{cm} \doteq 4.4721 \ \text{cm} \ \\ u_{2}=\sqrt{ a^2 + u_{1}^2 }=\sqrt{ 3^2 + 4.4721^2 } \doteq \sqrt{ 29 } \ \text{cm} \doteq 5.3852 \ \text{cm} \ \\ \ \\ x=u_{1}=4.4721=2 \ \sqrt{ 5 }=4.472 \ \text{cm}

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