[tex]\displaystyle \\
h = 2b+5 ~~\Longrightarrow~~ 2b = h-5 ~~\Longrightarrow~~ \boxed{b = \frac{h-5}{2}} \\ \\
A = 21 \\ \\
A=\frac{b \times h}{2}\\\\
21 = \frac{b \times h}{2}\\\\
21 = \frac{\frac{h-5}{2} \times h}{2}\\\\
42=\frac{h-5}{2} \times h\\\\
42=\frac{h(h-5)}{2}\\\\
84=h(h-5) \\
h^2 -5h -84=0 \\
(h+7)(h-12)=0 \\
\Longrightarrow~~h+7=0 ~~or~~h-12 = 0\\
h+7 = 0 ~~\Longrightarrow~~h=-7~~~unacceptable ~~because -7 \ \textless \ 0\\
h-12 = 0 ~~\Longrightarrow~~\boxed{h=12}[/tex]
