Question 799786
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The length of the longest stick would be the hypotenuse of a right triangle where the legs are the height of the cube and the diagonal across the base of the cube.


The diagonal across the base of the cube is the hypotenuse of an isosceles right triangle with legs measuring 10, therefore having a length of *[tex \LARGE 10\sqrt{2}].  Verification by use of Pythagoras left as an exercise for the student.


The hypotenuse of a right triangle with legs of *[tex \LARGE 10\sqrt{2}] and *[tex \LARGE 10] is given by:


*[tex \LARGE \sqrt{10^2\ +\ (10\sqrt{2})^2}]


Arithmetic left as an exercise for the student.  Left in radical form, this is the exact answer presuming that the "stick" has a zero thickness, in other words has the dimensions of a geometric line.  Any thickness at all would have to be accounted for by other computations that are somewhat more complex than those presented here.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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