make a drawing

let 'a' represent the measure of the side of the square

the length of the side of the square is equal to the diameter of the square

the perimeter of the square is: P1 = 4a

the circumference of the circle is: P2 = a*pi (since the circumference of the circle is diameter x pi, and in our case the diameter = a)

the perimeter of the square exceeds the circumference of the circle by 10 units:

P1 = 10 + P2

4a = 10 + a*pi

4a - a*pi = 10

a(4 - pi) = 10

a = 10/(4 - pi)

pi = 3.14

a = 10/(4 - 3.14)

a = 11.63 units

the measure of the side of the square is 11.63 units.