SOLUTION
The area of triangle ABC in terms of a and b is:
[tex]A=\frac{1}{2}ab[/tex]
The area of triangle ABC in terms of c and h is:
[tex]A=\frac{1}{2}ch[/tex]
Equating the areas gives:
[tex]\frac{1}{2}ab=\frac{1}{2}ch[/tex]
Isolating h gives:
[tex]\begin{gathered} ab=ch \\ h=\frac{ab}{c} \end{gathered}[/tex]
Hence the prove.
