The length of the rectangle is 42 cm, and the width is 24 cm.
Let the length of the rectangle be \(7x\) and the width be \(4x\), where \(x\) is a positive constant. The given information is that the ratio of the length to the width is \(7:4\).
The perimeter of a rectangle is given by \(P = 2l + 2w\), where \(l\) is the length and \(w\) is the width.
\[ P = 2(7x) + 2(4x) \]
\[ 132 = 14x + 8x \]
\[ 22x = 132 \]
\[ x = 6 \]
Now that we have the value of \(x\), we can find the length and width:
Length (\(l\)) = \(7x = 7 \times 6 = 42\) cm
Width (\(w\)) = \(4x = 4 \times 6 = 24\) cm
Therefore, the length of the rectangle is 42 cm, and the width is 24 cm.