SOLUTION: The perimeter of a parallelogram ABCD IS 92cm. AD is 1cm more than twice AB. Find the lengths of all four sides of ABCD

Let x = |AD|   (the length of the side AD).
Let y = |AB|   (the length of the adjacent side AB).

Then 

2x + 2y = 92   (the perimeter)
 x - 2y = 1    ("AD is 1cm more than twice AB.")

Add the two equations (both sides) and get

3x = 92 + 1  --->  3x = 93  --->  x =   --->  x = 31.

Then from the second equation  2y = x - 1 = 30-1 = 30.
Hence, y =  = 15.

Answer. The sides of the parallelogram are 31, 15, 31 and 15 cm long.