Answer
$10.9\;cm$.
Work Step by Step
The given values are:
Area $A=120\;cm^2$.
Height $=h$
Base $=2h$
Formula for the area of the triangle.
$\Rightarrow A=\frac{1}{2}\times Height \times Base$
Substitute all values.
$\Rightarrow 120\;cm^2=\frac{1}{2}\times h \times 2h$
Simplify.
$\Rightarrow 120\;cm^2=h^2$
Take the square root on both sides.
$\Rightarrow \sqrt{120\;cm^2}=\sqrt{h^2}$
Simplify.
$\Rightarrow 10.9\;cm=h$.
