We know the diameter of the plate is 8 in. Since the cheese covers the entire plate, we also know the diagonal of the square is also 8in. We can use the pythagorian theorem to calculate the length of the side (remember that both sides are equal)
[tex]a^2 + a^2 = 8^2 \\ 2a^2 = 64 \\ a^2 = 32 \\ a = \sqrt{32} = 4\sqrt{2} = 5.66[/tex]
