Three pentagram-shaped stars (the stars formed from the diagonals of a regular pentagon) are stacked up so that the bottom two ends of the tips touch the middle ends of the tips of the star below. (See diagram.)

The distance from the top of the stack to the floor (where the bottom star's "feet" rest) is 4 feet.

What is the distance between the bottom two ends of the tips of the stack that touch the floor?

There have been other respondents who will have believed that they have solve this problem, otherwise some direction is obviously needed.

I drew this ‘stack’ in AutoCad (a high level drafting program) and then by proportion of the distance between the ‘feet’ of my ACAD drawing to the height of the stack, against the given height of 4 units, the distance between the feet was …     .613625.. units.

 Two other respondents (Nikki – ‘Really Long Explanation’ and vectorboy – ‘check’) have proposed the same result; myself twice (“Parallel Intercepts …..  & this, my ACAD verification).

 Have we misinterpreted something in the problem, or have our respective solutions been overlooked?

Posted by brianjn on 2004-07-16 04:18:31