Length = 18 cm Width = 8 cmStep-by-step explanation:As per the provided information in the given question, we have :Perimeter of the RECTANGLE = 52 cmWidth = 2 cm more than one-third of the length.We are asked to calculate the DIMENSIONS of the rectangle (length & width).Let the length of the rectangle be l. Then, according to the question, the width is 2 cm more than one-third of the length.In order to calculate the dimensions of the rectangle, we'll be using the formula of the perimeter of the rectangle, which will act as a LINEAR equation here to calculate the unknown values.As we KNOW that,As per question substitute the values.Substitute the value w in the terms of l.Performing simplification in the brackets.Performing addition in the brackets.Removing the brackets.Performing addition in the curly brackets.Transposing 2 from RHS to LHS and performing addition in RHS.Transposing 3 from RHS to LHS.Performing MULTIPLICATION in LHS.Now, transposing 6 from RHS, its sign will get changed.Performing subtraction in LHS.Transposing 4 from RHS to LHS. Its arithmetic operator will get changed.Dividing 72 by 4.∴ Length of the rectangle is 18 cm.Finding the width :According to the statement given in the question,Substitute the value of length to calculate the value of width.Performing multiplication in RHS.Performing addition.∴ Width of the rectangle is 8 cm.Therefore,⠀⠀⠀⠀⠀⠀★ Length = 18 cm⠀⠀⠀⠀⠀⠀★ Width = 8 cm