# What Can We Equate?

Geometry Level 5

The lengths of three sides of $$\triangle ABC$$ are $$AB=a+3b$$, $$BC=a+2b$$, and $$CA=a+b$$ where $$a$$ is a positive integer and $$0<b\leq 1$$. If the length of the altitude to side $$BC$$ is $$a$$, find the number of triangles, no pair being similar, which satisfy the conditions.

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