Answer
$x=5$ $in$
Work Step by Step
Draw vertical and horizontal lines separating your figure into two rectangular regions in addition to square region.
The long rectangular region is $14$ by $x$, so its area is $14x$ $in²$, while the short one is $13$ by $x$, so its area was $13x$ $in²$.
The square is $x$ by $x$ so its area is $x^2$ $in²$.
The combined areas are : $14x + 13x+x^2 = 160$
$\Rightarrow x^2+27x-160=0$
$\Rightarrow (x-5)(x+32)=0$
$\Rightarrow x=5$ or $x=-32$ $\color{red}{rejected}$
$x=5$ $in$
