Answer
$\bf\text{The original square has 13 inch sides.}$
Work Step by Step
The original square has sides $\bf{x}$, and the new square has sides $\bf{x-4}$
The perimeter of the new square, $\bf{4(x-4)}$,
is $\bf{\dfrac{1}{2}}$ the perimeter of the original square, $4x$, plus $10$
Putting that all together in an equation we have:
$\bf{4(x-4)}$ = $\bf{(\dfrac{1}{2}(4x))+10}$
$\bf{4x-16}$ = $\bf{2x+10}$
$\bf{2x}$ = $\bf{26}$
$\bf{x=13}$
$\bf\text{The original square has 13 inch sides.}$
