Wall and body diagonals

Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m

Result

u₁ =  1.118 m
u₂ =  2.062 m
u₃ =  2.236 m
d =  2.291 m

Solution:

$a = 0.5 \ m \ \\ b = 1 \ m \ \\ c = 2 \ m \ \\ \ \\ u_{ 1 } = \sqrt{ a^2+b^2 } = \sqrt{ 0.5^2+1^2 } \doteq 1.118 = 1.118 \ \text { m }$

$u_{ 2 } = \sqrt{ a^2+c^2 } = \sqrt{ 0.5^2+2^2 } \doteq 2.0616 = 2.062 \ \text { m }$

$u_{ 3 } = \sqrt{ b^2+c^2 } = \sqrt{ 1^2+2^2 } = \sqrt{ 5 } \doteq 2.2361 = 2.236 \ \text { m }$

$d = \sqrt{ a^2 + b^2 + c^2 } \ \\ \ \\ d = \sqrt{ u_{ 1 }^2 + c^2 } = \sqrt{ 1.118^2 + 2^2 } \doteq 2.2913 = 2.291 \ \text { m }$

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