Captain Taffle
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#1
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Triangle A and Triangle B are similar and have the same orientation. Triangle A is a subset of Triangle B (what I mean is Tri A is inside Tri B) as well as half its area, a line called L is drawn so that it crosses through both triangles such that Triangle A has been split into 30 % and 70% of its area. When L is drawn this condition must be satisfied.

1. Can you position Triangle A & B , and draw line L such that Triangle B is split into 50 %and 50%?

2. Can the same be done for 1. but with Triangle B being split into 40% and 60 %

3. What are the ranges of "partitions". For example : 50 % and 50% being the minimum and 0% and 100 % being the maximum

4. Bonus questions: did I explain this correctly ? is what I've proposed ill-defined ? is this actually a fun question ?
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username4899406
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interesting but we would have to see the orientation of both triangles first i think?
or is that part of the q as well?
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Captain Taffle
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Sorry for the slow reply,

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In short , I'm not sure. Both images above are valid examples of the same problem, I'd use the first image as its nice on the mind.
Let me know if that sets you in the right direction.

However I have to admit that I don't know the answer to even part 1. I am curious to see how people approach this, it could very well be the case that what I'm proposing is not well defined enough to solve. If it is the case , I welcome some guidance on what is missing
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Captain Taffle
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oh just to note, the area's in the images are indicative,
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mqb2766
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(Original post by Captain Taffle)
Sorry for the slow reply,

Name:  SnipALPHA.PNG
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Size:  39.8 KB
Name:  SnipALPHA2.PNG
Views: 4
Size:  29.7 KB

In short , I'm not sure. Both images above are valid examples of the same problem, I'd use the first image as its nice on the mind.
Let me know if that sets you in the right direction.

However I have to admit that I don't know the answer to even part 1. I am curious to see how people approach this, it could very well be the case that what I'm proposing is not well defined enough to solve. If it is the case , I welcome some guidance on what is missing
I guess when setting a question, it does help for there to be some structure/progression in the question. What age were you expecting to aim it at / what are you trying to ask about?

From a quick sketch (assuming the line is parallel to one side so you can exploit the similar property) both look possible, just by considering the area ratio at extreme positions of the interior triangle and arguing that it must change continuously as you move it. But Im not really getting any great insight.

Gut feeling is that it would be heavy going to consider lines not parallel to a side and the continuity argument about things changing smoothly probably means you dont have to.
Last edited by mqb2766; 3 weeks ago
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