C

Step 1: Two traingles are said to be congruent, if all the angles and the corresponding sides of the two traingles are equal.

Step 2: The measure of BC = measure of QR, measure of BD = measure of PQ and measure of DC =measure of PR.[ΔPQR and ΔDBC are congruent.]

Step 3: So, QR = 8 cm, PR = 4 cm and PQ = 6 cm.

Step 4: Similarly, measure of XY = measure of AB, measure of XZ = measure of AD and measure of YZ = measure of BD[ΔXYZ and ΔABD are congruent.]

Step 5: So, XY = 3 cm, XZ = 5 cm and YZ = 6 cm.

Step 6: Perimeter of ΔPQR = sum of lengths of all the sides of the ΔPQR = PQ + QR + PR = 6 + 8 + 4 = 18 cm

Step 7: Perimeter of ΔXYZ = sum of lengths of all the sides of the ΔXYZ = XY + XZ + YZ = 3 + 5 + 6 = 14 cm

Step 8: Sum of the perimeters of the ΔPQR and ΔXYZ = Perimeter of ΔPQR + Perimeter of ΔXYZ = 18 + 14 = 32 cm