The length of a diagonal of a square is 8 mm. Find the perimeter of the square.

15.39 mm

22.8 mm

7.7 mm

32 mm

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