Answer
The value of $x$ is $8$.
Work Step by Step
Height of the triangle $h=\sqrt{3x+12}\;ft$.
Base of the triangle $b=2\;ft$.
Area of the triangle $A=\sqrt{5x-4}\;ft^2$.
Formula for the area of the triangle.
$\Rightarrow A=\frac{1}{2}bh$
Substitute the given values.
$\Rightarrow \sqrt{5x-4}=\frac{1}{2}(2)(\sqrt{3x+12})$
Simplify.
$\Rightarrow \sqrt{5x-4}=\sqrt{3x+12}$
Square each side of the equation.
$\Rightarrow (\sqrt{5x-4})^2=(\sqrt{3x+12})^2$
Simplify.
$\Rightarrow 5x-4=3x+12$
Add $4-3x$ to each side.
$\Rightarrow 5x-4+4-3x=3x+12+4-3x$
Simplify.
$\Rightarrow 2x=16$
Divide each side by $2$.
$\Rightarrow x=8$
Hence, the value of $x$ is $8$.
