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.

Correct answer:

u₁ =  5 cm
u₂ =  12.3693 cm
u₃ =  12.6491 cm
d =  13 cm

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ b=3\text{ cm } \\ c=12\text{ cm } \\ {u}_1=\sqrt{a^2+b^2}=\sqrt{4^2+3^2}=5\text{ cm} \end{gathered}$$

$u_2=\sqrt{b^2+c^2}=\sqrt{3^2+12^2}=3\sqrt{17}=12.3693\text{ cm}$

$u_3=\sqrt{a^2+c^2}=\sqrt{4^2+12^2}=4\sqrt{10}=12.6491\text{ cm}$

$d=\sqrt{a^2+b^2+c^2}=\sqrt{4^2+3^2+12^2}=13\text{ cm}$

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