In Session 41 (Advanced Example), dealing with the Lagrange Multipliers. There was a triangular pyramid. To find the slant height of one of the sides, Dr. Auroux made it into the hypotenuse of the right triangle formed by the pyramid height (PQ) and a line on the base triangle to the side (which he called "u_"). My Question: Dr. Auroux assumed that line segments u_1, u_2, and u_3 were perpendicular to the sides of the base triangle. This fact helped him find the area of the base triangle later, but how can he assume that? How do we prove that the "u"s are perpendicular?

Question

In Session 41 (Advanced Example), dealing with the Lagrange Multipliers.  There was a triangular pyramid.  To find the slant height of one of the sides, Dr. Auroux made it into the hypotenuse of the right triangle formed by the pyramid height (PQ) and a line on the base triangle to the side (which he called "u_<number>").

My Question:

Dr. Auroux assumed that line segments u_1, u_2, and u_3 were perpendicular to the sides of the base triangle.  This fact helped him find the area of the base triangle later, but how can he assume that? How do we prove that the "u"s are perpendicular?

experimentx · Answer

geometry
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experimentx · Answer

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anonymous · Answer

I think you misunderstood me.  I meant the u's as in the heights ON THE BASE TRIANGLE.  Not the slant heights.

experimentx · Answer

can you give me lecture no?

anonymous · Answer

He does the example at 38:00. Thank you! I really appreciate it. http://www.youtube.com/watch?v=15HVevXRsBA&feature=BFa#t=38m

experimentx · Answer

i'll try to rely as fast as i can ... if i can.

anonymous · Answer

I just don't know how he makes the assumption that the segments from Q to the sides are perpendicular at 45:10.

anonymous · Answer

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How are those segments on the base perpendicular?