Question

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

Answer 1

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