MHB Find Length X in Triangle: Learn How to Calculate It

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The discussion centers on calculating the length x in a triangle where FH and HC are perpendicular. Participants express confusion about the problem and seek clarification on the relationships between the triangle's components. A hint is provided regarding the similarity of triangles, suggesting that identifying similar triangles can lead to the solution. The calculation involves the ratio x = 4 * CF / BF, which helps in finding the length. The conversation highlights the importance of understanding triangle properties to solve the problem effectively.
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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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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