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All integers (Posted on 2005-01-17) Difficulty: 3 of 5
The sides of a trapezoid are 5, 8, 11, and 13, and its diagonals are also integer numbers; what are they?

See The Solution Submitted by Federico Kereki    
Rating: 4.5000 (2 votes)

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re: Solution | Comment 7 of 14 |
(In reply to Solution by Fletch)

The first line of my 3-line table is a figure-8:

top "bot"left rt    d1  d2    alt       left over  rt over     calc bottom
  8   5  13  11      9   9    8.87412    -9.50000  -6.50000     -8.000000

The -8 calculated bottom length indicates (1) by its negative sign that it is indeed a figure-8 type and (2) the bottom is of length 8 rather than the hoped-for 5.  So the top and the bottom are both 8 and it's a figure-8 style.  The side of length 13 extends from the top left to the bottom right, even past (by 1.5 units) the right end of the top. The side of length 11 extends from the top right to the bottom left, but not quite (short by 1.5 units) to being directly under the left side of the top.

The diagonals in this instance are external, and what would look like the sides of a different trapezoid, and are both of lenght 9: one forming an obtuse angle at the bottom and the other forming an obtuse angle at the top.

In fact, looking at the figure with the length-9 segments forming sides (as opposed to diagonals of a figure-8 type), the diagram is a parallelogram of sides 8 and 9, with diagonals of 11 and 13.

  Posted by Charlie on 2005-01-18 13:19:50
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