let h be height and b the base. So we get that
[tex]\begin{gathered} \frac{h\cdot b}{2}=27\rightarrow h\cdot b=54 \\ h=2b-3 \end{gathered}[/tex]so we get that
[tex]\begin{gathered} (2b-3)b=54 \\ 2b^2-3b-54=0 \\ (b-6)(2b+9)=0 \end{gathered}[/tex]as b must be positive, we get that b=6, and therefore h=12-3=9
