MHB Can a Triangle Be Divided Into 205 Congruent Triangles?

Albert1
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Prove that there exists a triangle which can be cut into 205 congruent
triangles.
 
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Albert said:
Prove that there exists a triangle which can be cut into 205 congruent
triangles.
hint:
Suppose that one side of a triangle has length $n$. Then it can be cut into $n^2$
congruent triangles which are similar to the original one and whose corresponding sides to
the side of length $n$ have lengths 1.
$205=a^2+b^2$ here $a,b\in N$
find all possible $a$ and $b$
 

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