Hi Samantha S

20 cm

If your question is referring to a diagonal that splits the square into two equal right triangles, then the length is 20 cm. Please see below

According to the information you have a Square with an area of 200 cm^{2}

The Area Square is s^{2} and a square has 4 right angles

So the length of any side in your square is the square root of the area.

s = √200

s = 10√2

If your question is referring to a diagonal that splits the Square into two equal right triangles then you can use the Pythagorean theorem to calculate the length of the diagonal or hypotenuse of the Right Triangle formed

(10√2)^{2} + (10√2)^{2} = (Length of the diagonal)^{2}

200 + 200 = (Length of the diagonal)^{2}

400 = (Length of the diagonal)^{2}

To find the length we take the square root of 400

√400 = Length of the diagonal

20 = Length of the diagonal

If your question is referring to another diagonal, then a picture or diagram would be appreciated and maybe we can try and help you further.