Square Inscirbed in a Triangle

There is a square inscribed in a 3 - 4 -5 right angled triangle. That is, the opposite is 3cm, the adjacent is 4cm and the hypotenuse is 5cm.

There is a diagram, here is an attempt to describe it: The square is situated such that two of it's sides are parts of adjacent and opposite, and the other two sides go from the opposite to meet the hypotenuse, and then down from that point to meet the adjacent.

I'll attempt to draw it...

Code:

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What fraction of the triangle does the square occupy?

My uncle says that all of the triangles are scalar multiples of each other, so they all have the same tangents (same opp/adj), then he worked it out from there, but I can't see how he got this?