The Belt Doubt!

Algebra Level 2

A magic wish-granting rectangular belt always shrinks to \( \frac 1 2 \) its length and \( \frac 1 3 \) its width whenever its owner makes a wish. After three wishes, the surface area of the belt's front side was \(4 \text{ cm}^2 \).

If the original width was \(9 \text{ cm} \), what was the original length in \( \text{cm} \)?

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