Answer
Perimeter: $12x^{1/3}$
Area: $6x^{2/3}$
Work Step by Step
First we determine the hypotenuse of the triangle, using the Pythagorean formula:
$$\sqrt{(3x^{1/3})^2+(4x^{1/3})^2}=\sqrt{25x^{2/3}}=5x^{1/3}.$$
We find the perimeter of the triangle:
$$\begin{align*}
\text{Perimeter}&=3x^{1/3}+4x^{1/3}+5x^{1/3}\\
&=12x^{1/3}.
\end{align*}$$
We find the area of the triangle:
$$\begin{align*}
\text{Area}&=\dfrac{(3x^{1/3})\cdot (4x^{1/3})}{2}\\
&=6x^{2/3}.
\end{align*}$$
