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#1**+1 **

Expanding the terms,

\((x^2+2xh+h^2)+(y^2+2yh+y^2)=(a^2+2ab+b^2) \)

Using Pythagorean Theorem,

\(x^2+h^2=a^2\\ y^2+h^2=b^2\)

We could subsitute the values in, and rewrite the equation

\(a^2+2xh+b^2+2yh=a^2+2ab+b^2\\ 2xh+2yh=2ab\\ h(x+y)=ab \)

\([ABC]=\frac12 AB\cdot CH = \frac12 BC \cdot AC\\ \frac12 (x+y)h=\frac12 ab\\ h(x+y)=ab\)

I hope this helped,

Gavin

GYanggg Oct 30, 2018