Find Length X in Triangle: Learn How to Calculate It

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Discussion Overview

The discussion revolves around finding the length x in a triangle where certain segments are perpendicular. Participants express confusion and seek clarification on the relationships between the triangle's sides and angles, as well as the implications of given lengths.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant states they are stuck on finding the length x and believes the answer should be 5, but does not know how to arrive at that conclusion.
  • Another participant questions whether the perpendicularity of segments FH and HC implies that angle CHF is 90 degrees, expressing frustration with the clarity of the original post.
  • A participant suggests considering similar triangles as a hint to solve for x, noting that two triangles are similar if they share two angles.
  • Another response indicates that once the hint is understood, x can be expressed as x = 4 * CF / BF, implying a relationship between the segments.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the method to find x, with multiple interpretations and approaches being discussed.

Contextual Notes

There are unresolved assumptions regarding the triangle's configuration and the relationships between the segments, which may affect the clarity of the problem.

ketanco
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what is the length x? (FH and HC perpendicular too, which I missed to write)
I am totally stuck can not make any progress on this question. Answer should be 5. I don't know how to obtain it

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ketanco said:
FH and HC perpendicular too
Does that mean that angleCHF = 90?
Your writing is terrible!
AB = 9 and EF = 4?

Not important but why is there no point G (you jumped from F to H!)
 
ketanco said:
what is the length x? (FH and HC perpendicular too, which I missed to write)
I am totally stuck can not make any progress on this question. Answer should be 5. I don't know how to obtain it

Hint: Which triangles are similar to each other?
(Two triangles are similar if they have 2 angles in common.)
 
Once you get Klaas' hint, you should "see" that x = 4 * CF / BF
 

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