\[ a + b = 14 \]

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• Let the legs of the right triangle be \(a\) and \(b\), and the hypotenuse \(c = 10\). The radius \(r\) of the inscribed circle is given by:
• Given that \(r = 2\), we have:
• \[ 2 = \frac{a + b - 10}{2} \]
• The area \(A\) of the triangle is given by:
• \[ A = \frac{1}{2}ab \]
• Using the Pythagorean theorem:

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