By definition, Perimeter means the sum of the sides. Given that the shape is a rectangle we know that it has two pairs of congruent sides. The difference between the total perimeter and the first pair of sides leaves the sum of the other pair of congruent sides. Since they are congruent then each the second pair must be equal must be the same so algebra at that point:
P_rectangle = side 1 + side2+ side 3+ side 4 given
Side 1= side 2 definition of rectangle
Side 3 =side4 definition of rectangle
P = 36 cm (given)
Let side1 = 10 cm given
Side2 = side 1= 10cm
36 = 10cm + 10cm + side3 +side 4
36= 20 + 2 (side 3)
16 = 2(side 3)
Side 3 = 8
Check to verify
36 = 10+10+8+8
36=36