The length of a rectangle is 4 cm longer than its width: if the perimeter of the rectangle is 52 cm, find its length and width.
Let's call the width of the rectangle x cm.
According to the problem, the length of the rectangle is 4 cm longer than its width, so the length would be x + 4 cm.
The perimeter of a rectangle is given by the formula 2(length + width).
Therefore, the perimeter of this rectangle is 2(x + 4 + x).
Simplifying the expression, we have 2(2x + 4).
Expanding, we have 4x + 8.
Since we are given that the perimeter is 52 cm, we can set up the equation 4x + 8 = 52.
Subtracting 8 from both sides, we have 4x = 44.
Dividing both sides by 4, we have x = 11.
Therefore, the width of the rectangle is 11 cm, and its length is x + 4 = 11 + 4 = 15 cm. Answer: \boxed{11, 15}.