Area........Perimeter

Geometry Level 5

\(\color{red}{\Delta ABC}\) is a right angled triangle with integral sides \(\color{orange}{a}\), \(\color{pink}{b}\), and \(\color{green}{c}\), having the special property that the area of the triangle is numerically double its perimeter.

Determine the maximum possible area of \(\color{blue}{\Delta ABC}\).

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