Answer:
20√2 cm
Explanation:
The diagonal of a square forms a right triangle with it's 2 sides.
Going step by step, lets refer to the side of a square as x.
Our triangle will have 2 legs of x and a diagonal of 10. We can either use the 45:45:90 method or use Pythagorean. The 45:45:90 method is more simpler so I will show the step by step method through Pythagorean, which the 45:45:90 method is derived from anyways.
x^2 + x^2 = 10^2
2x^2 = 100
x^2 = 50
x = √50 = 5√2
The perimeter is equal to the sum of all the square's sides, which modeled by x would equal 4x.
so the perimeter would be 4 * 5√2 which is 20√2
Hope this helps :)