Answer
$13~\text{in}\times 13~\text{in}$
Work Step by Step
Let the side of original square is $x$.
Perimeter will be: $4x$
New side of square: $(x-4)$
New perimeter: $4(x-4)$
Form the equation according to task:
$$4(x-4)=\frac{4x}{2}+10$$
$$4x-16=2x+10$$
$$4x-2x=10+16$$
$$2x=26$$
$$x=13$$
