Step 1 :The problem states that the length of a rectangle is three times its width. We can express this as \(length = 3 \times width\).
Step 2 :We are also given that the perimeter of the rectangle is 72 cm. The formula for the perimeter of a rectangle is \(2 \times (length + width)\).
Step 3 :Substituting the expression for length from step 1 into the perimeter formula, we get \(2 \times (3 \times width + width) = 72\).
Step 4 :Solving this equation for width, we find that \(width = 9 cm\).
Step 5 :Substituting \(width = 9 cm\) back into the expression for length, we find that \(length = 3 \times 9 cm = 27 cm\).
Step 6 :Final Answer: The width of the rectangle is \(\boxed{9 cm}\) and the length of the rectangle is \(\boxed{27 cm}\).