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

Correct answer:

u₁ =  1.118 m
u₂ =  2.0616 m
u₃ =  2.2361 m
d =  2.2913 m

Step-by-step explanation:

$$\begin{gathered} a=0.5\text{ m } \\ b=1\text{ m } \\ c=2\text{ m } \\ {u}_1=\sqrt{a^2+b^2}=\sqrt{0.5^2+1^2}=1.118\text{ m} \end{gathered}$$

$u_2=\sqrt{a^2+c^2}=\sqrt{0.5^2+2^2}=2.0616\text{ m}$

$u_3=\sqrt{b^2+c^2}=\sqrt{1^2+2^2}=\sqrt{5}=2.2361\text{ m}$

$$\begin{gathered} d=\sqrt{a^2+b^2+c^2} \\ d=\sqrt{u_1^2+c^2}=\sqrt{1.118^2+2^2}=2.2913\text{ m} \end{gathered}$$

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