The diagonal of a square is given by:
d = root ((L) ^ 2 + (L) ^ 2)
Where,
L = side of the square.
So we have to clear L:
d ^ 2 = (L) ^ 2 + (L) ^ 2
d ^ 2 = 2 (L) ^ 2
(L) ^ 2 = (d ^ 2) / 2
L = root ((d ^ 2) / 2)
Substituting
L = root (((8) ^ 2) / 2) = 5.66 mm
Then, the perimeter of the square is given by:
P = 4L = 4 * (5.66) = 22.64mm
answer
The perimeter of the square is 22.64mm or
22.8 mm
