# Cube diagonal

Determine the length of the cube diagonal with edge 37 mm.

Result

d =  64.086 mm

#### Solution:

$a=37 \ \text{mm} \ \\ s^2=a^2+a^2=2a^2 \ \\ \ \\ d^2=a^2 + s^2 \ \\ d^2=a^2 + 2a^2 \ \\ d^2=3a^2 \ \\ \ \\ d=\sqrt{ 3 } \cdot \ a=\sqrt{ 3 } \cdot \ 37 \doteq 37 \ \sqrt{ 3 } \doteq 64.0859 \doteq 64.086 \ \text{mm}$

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