The length of side AD in rectangle ABCD, with AB = 21 and BC = 12, is 12 units. The perimeter is 66 units, determined by 2(21 + 12).
Let's denote the length of side AD as x. The perimeter (P) of a rectangle is given by the formula:
P = 2(length + breadth)
Given that the perimeter is 66 units and the length and breadth are expressed in terms of z:
66 = 2(3z + 3 + 2z)
Now, solve for z:
66 = 2(5z + 3)
33 = 5z + 3
30 = 5z
z = 6
Now that we know z, substitute it back into the expressions for the length and breadth:
Length (AB) = 3z + 3 = 3(6) + 3 = 21
Breadth (BC) = 2z = 2(6) = 12
Since AD is the same as BC in a rectangle, AD = 12.