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#1 2006-10-12 19:19:09

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Hard(ish) Geometry problem 2

Hi everyone,
I've been wrestling this problem for some time now, but every solution I try seems to not work (My worst subject is probably geometry -_-). (This problem is also in excercises)

Question:
Ribbon is run around a box so that it makes a complete loop with two parallel pieces of ribbon on the top (and on the bottom) of the box.

The ribbon crosses every face once, except the top and bottom, which it crosses twice. The ribbon rests tightly against the box all the way round because the angle at which it meets a corner is continued onto the next face.

I can cut the ribbon in advance of placing it around the box and I can slide the ribbon around a little to position it.

If the box is 20cm by 10cm by 5cm, how long will the ribbon be?

Last edited by Toast (2006-10-12 19:54:53)

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#2 2006-10-12 22:24:45

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Hard(ish) Geometry problem 2

Hi, this angle being the same at each edge is a cool concept!!  I never thought of that before!!


igloo myrtilles fourmis

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#3 2006-10-12 22:48:49

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Hard(ish) Geometry problem 2

Huh? All the angles in the ribbon are the same? I'm so confused -.-

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#4 2006-10-13 20:33:25

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Hard(ish) Geometry problem 2

Anyone?

Is this even solvable?

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#5 2006-10-16 23:10:25

tonydot11
Guest

Re: Hard(ish) Geometry problem 2

hi
if you start with aset distance in from each corner you can reduce the problem to 3 triangles and using pythagorus you can ascertain the hypothanuse of each triangle then multiply by the by the number you need. i took a measurement of 5 cm on long sides and 2.5 on the short sides of the cuboid which gave me 3 congruent trinagles one on each side of the long sides one on each sides of the short sides then two on top and bottom so giving eight hypothanuse which worked out to ans 58.988cm length of ribbon
roflol

#6 2006-10-17 19:49:12

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Hard(ish) Geometry problem 2

Hi tony,
I'm afraid I only understand about half of your solution. Could you please tell me how you came up with the measurements of 5 and 2.5? Thanks.

Anyway, I have my own (probably much more confusing) solution which I just found out today. It involves making the prism into a net and using pythagoras there. I'll post it as soon as I get the problem sheet back (it's not fresh in my mind). big_smile

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