The area of the rectangle is 432 cm².
The rectangle contains 12 squares with the same area. Then, the area of each square is:
432 cm²/12 = 36 cm²
The area of a square is A = l², then, the length of the side of each square is:
l = √A
l = √(36 cm²) = 6 cm
You can notice that the width of the rectangle is constituted by four squares, then, the with of the rectangle is:
w = 4l = 4(6 cm) = 24 cm
The height of the rectangle is constituted by three squares:
h = 3(6 cm) = 18 cm
Finally, the perimeter of a rectangle is given by the following formula:
P = 2w + 2h
by replacing the values of w and h you obtain:
P = 2(24 cm) + 2(18 cm)
P = 48cm + 36cm
P = 84 cm
Hence, the perimeter of the rectangle is 84 cm