Josh K.

asked • 06/23/17

Question about how diagonals in a cube works

In a cube with edges of length 6 units. Points M and N are the midpoints of the two edges of the cube, M is located at the front bottom middle of the cube and N at the right side middle of the back of the cube. What is the length of the line segment MN?
 
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Mark M. answered • 06/23/17

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Draw and label a diagram.
Point P is the corned directly below N
MP = √(32 + 62)
MP = √45
MN = √(32 + 45)
 
What is the length of MN?
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Josh K.

If P is corned on the vertex below N, wouldn't the triangle fail to be a right triangle and the pythagorean cannot be applied?
 
If P is corned at the imaginary space beneath N, how did we figure out the sides of the newly formed triangle?
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06/23/17

Mark M.

P is at a corner.
M and P lie in the same plane - the base of the cube. MP is the hypotenuse. Long side is an edge (6) and the short short side is one-half of an edge - M is the midpoint. Pythagoras holds.
MP becomes the long side of the triangle MPN. The short side is 3 (N is in the middle of a side) and the hypotenuse is MN, the length sought.
 
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06/23/17

Josh K.

Got it! Thank you so much! Turns out I've been interpreting the flat plane of the cube as a rise in height.
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06/23/17

Mark M.

You are welcome. Drawing a diagram is very helpful.
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06/23/17

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