In order to solve this problem, we first need to find the side lengths of the square. We know that the area of a square is one length squared, so we can set up this equation:
200 = [tex]sidelength ^{2} [/tex]
We solve this by taking the square root of both sides.
[tex]14.14 = sidelength[/tex]
So, one side of the square is 14.14cm. To finish this problem, we apply the pythagorean theorem. We can do this by drawing in the diagonal to make a triangle (shown in attachment - the blue part in the second drawing is the section that we use. Please note that the drawing is not to scale)
The pythagorean theorem is [tex] a^{2} + b^{2} = c^{2} [/tex], where c squared is the diagonal of a right triangle. A squared and b squared are the other two sides. We can now plug in our numbers.
[tex] 14.14^{2} +14.14^2=c^2=20[/tex]
So, the diagonal length is 20 cm.
