Answer
$(x-1)\text{ meters}$
Work Step by Step
Using $V=lwh$ or the formula for the volume of a rectangular box, then
\begin{array}{l}\require{cancel}
V=lwh
\\\\
x^4+6x^3-7x^2=(x+7)w(x^2)
\\\\
x^4+6x^3-7x^2=(x^3+7x^2)w
\\\\
\dfrac{x^4+6x^3-7x^2}{x^3+7x^2}=w
.\end{array}
Using the long division below, then
\begin{array}{l}\require{cancel}
w=\dfrac{x^4+6x^3-7x^2}{x^3+7x^2}
\\\\
w=x-1
.\end{array}
Hence, the width is $
(x-1)\text{ meters}
.$
