SOLUTION: Set up and solve the required proportion. The diagonal of a cube varies directly with the length of a side. Find the constant of proportionality.

Question 1136632: Set up and solve the required proportion.
The diagonal of a cube varies directly with the length of a side. Find the constant of proportionality.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The diagonal of a cube extends from one of its corners diagonally through the cube to the opposite corner, so it is the hypotenuse of a right triangle formed by the height of the cube and the diagonal of its base.
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therefore, we will use the Pythagorean Theorem twice to find the constant of proportionality
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let s be the length of the cube's side and x be the length of the diagonal of its base, then
:
x^2 = s^2 + s^2 = 2s^2
:
x = s * square root(2)
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now we can calculate the length of the cube's diagonal(d)
:
d^2 = (s * square root(2))^2 + s^2
:
d^2 = 2 * s^2 + s^2 = 3 * s^2
:
d = s * square root(3)
:
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the constant of proportionality is square root(3)
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