The perimeter of the joined figure will be the sum of the perimeters of rectangles A and B, less the lengths of the sides that are joined. The two joined sides have a total length of ...
(40 cm) +(40 cm) -(68 cm) = 12 cm
Then the length of the joined sides is 6 cm. The length of the other side of the rectangle is the difference between half the perimeter and this, or ...
(40 cm)/2 -6 cm = 14 cm
The length and width of rectangles A and B are 14 cm and 6 cm. When put together, they are joined on the 6 cm side.
