Alex owns one of those folding rulers where each segment is exactly 1 foot long. While playing with the open ruler he formed it into a triangle. Then he refolded it into a second triangle with double the area.
What is the smallest possible length of the ruler? What if the second triangle has 3 times the area?
I assumed that the ruler in could be configured in a long skinny pattern to give a particular area or reconfigured into a shorter, wider pattern to give double the area (case 1); or for a different ruler triple the area (case 2).
For a ruler {perimeter} of 20 feet,
{2,9,9} has Area 4√5 and
{6,6,8} has Area 8√5 (double)
For a ruler {perimeter} of 17 feet,
{1,8,8} has Area 3.992179855667828 and
{4,6,7} has Area 3*3.992179855667828 = 11.976539567003485
(triple)
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Posted by Larry
on 2024-06-27 14:55:29 |
Solution if I interpreted correctly.
