Question 1065070: In a parallelogram ABCD the lengths of the sides AD and AB are 8 in and 3 in respectively. Angle bisectors of angle A and angle D split the opposite side into three segments. Find the length of each of these segments.
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52864)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! Well-slept, on a Saturday morning, I have an interpretation and answer to that problem.
If you enter a thank-you note, could you tell me where the problem came from, and if my reading/interpretation of the problem is correct?
The segment lengths are  .
The text posted does not give enough information to identify what parallelogram ABCD looks like.
Is there a typo? Is it a poorly designed problem?
Assuming that it was a problem designed by an intelligent mind,
it took a less sleep-deprived mind to decipher what interpretation/reasoning/answer might be expected.
Below are two parallelograms that could be ABCD.
I did not label vertices, because it does not matter:
AD is one of the long sides, and AB is one of the short sides.
I split the parallelograms into 3 parallelograms.
The ones at the ends (where A and D are) are rhombi,
and the angle bisectors, contain AX and DY,
are diagonals of those rhombi.
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