#### Answer

Length = $x^{3}-2$

#### Work Step by Step

Factoring the expression for the area,
$7x^{4}-14x=7x\cdot x^{3}-7x\cdot 2$
$=7x\cdot(x^{3}-2)$
Since the area of a rectangle equals (length)$\times$(width),
and one factor of the area is $7x$, the width,
it follows that the other factor must be the length.
Length = $x^{3}-2$.