Answer:
16
Step-by-step explanation:
You can use the pythagorean theorem:
[tex]a^{2}+b^{2}=c^{2}[/tex], here seeing as we know already know two sides here as all sides are congruent with squares and there has to be right angles for it to be a square we can do so by cutting the square in half for the diagonal and to get a right triangle.
And from there we just use it:
[tex]8\sqrt{2}^{2} + 8\sqrt{2}^{2} = c^{2}[/tex]
[tex]\sqrt{128}^{2} + \sqrt{128}^{2} = c^{2}[/tex]
[tex]128 + 128 = c^2[/tex]
[tex]256 = c^2[/tex]
[tex]\sqrt{c}^2 = \sqrt{256}[/tex]
[tex]c = 16[/tex]
Meaning that the diagonal is 16.
