To begin, the total of the perimeters of rectangles X Y and Z is 46 cm. This is equal to 2(A+B+C+2D+E). So A+B+C+2D+E is 23 centimetres. If we can find the value of D, we can solve the problem. Knowing that rectangles X and Y have equal perimeters and X and Z have equal areas, we can form a system of equations below. There are only 2 possible values of D, 3 cm and 13 cm. 13 cm obviously doesn’t work. D=3, and so A+B+C+D+E = 20 cm.
A+B=C+D\\AB=DE\\A+B+C+2D+E=23\\AB+CD+DE=39\\[8pt] \\D(C+2E)=39\\C,D,E\in\Z\\\Rightarrow D=3