Answer
$\color{blue}{\bf\text{(a) }x^2\sqrt{3}}$
$\color{blue}{\bf\text{(b) } 64\sqrt{3}\text{ square units} }$
Work Step by Step
If the area of an equilateral triangle with side length $x$ is the function:
$A(x)=\dfrac{\sqrt{3}}{4}x^2$
$\bf(a)$ The formula for a triangle with twice the original side length is:
$\dfrac{\sqrt{3}}{4}4x^2$
$A(2x)=\color{blue}{x^2\sqrt{3}}$
$\bf(b)$ Using the formula above, we will find the area of a triangle with side lengths $16$:
$A(2x)=x^2\sqrt{3}$
$2x=16$
$x=8$
$8^2\sqrt{3}$
$A(16)=\color{blue}{64\sqrt{3}\text{ square units}}$
