The area of a rectangle has a formula of
A = LW
where L is the length and W is the width of the rectangle. Since it is mentioned in the problem that the length is bigger than the width by 4 cm,
L = 4 + W
Substituting this to the area formula:
360 cm² = (4 + W)(W)
Solving for W,
W = 17.08,-21.08
Since it is a quadratic formula, there are two roots. We use the positive root as the answer. So, W = 17.08 cm. Then,
L = 4 + 17.08 = 21.08 cm
Thus, the dimensions of the rectangle are 21.08 cm long and 17.08 cm wide.