SOLUTION: find the length of a diagonal of the cube with 3cm side length

Question 1116781: find the length of a diagonal of the cube with 3cm side length

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let s be the length of a side, then use Pythagorean Theorem to get the diagonal(h) across the base
:
s^2 + s^2 = h^2
:
Use Pythagorean Theorem again to get the cube's diagonal(d)
:
h^2 + s^2 = d^2
:
substitute for h^2
:
s^2 + s^2 + s^2 = d^2
:
3s^2 = d^2
:
d = square root(3s^2) = s * square root(3)
:
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cube diagonal is 3 * square root(3) approximately 5.2 cm
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