Rectangle Dimensions Uncovered: Find the Area When a Side is X + 6

To solve this problem, we need to compute the area of the rectangle using its side lengths and check which of the given choices matches this computation.

The rectangle has two sides: the smaller side $X$ and the larger side $X + 6$. Therefore, the area $S$ of the rectangle is given by:

$S = X \cdot (X + 6) = X^2 + 6X$

We need to connect this expression for $S$ with one of the statements describing a relationship involving a shifted value, which most likely involves some manipulations such as transformations. Let's reconsider the given choices.

The choice identified as: $\text{9+S equal to the smaller side plus 3 squared (the two squared).}$ essentially hints at forming a perfect square that corresponds to a known algebraic identity or transformation.

Notice the expression: $X \cdot (X + 6) = X^2 + 6X$ can be further expanded optionally in known square terms:

$= (X + 3)^2 - 9$

This algebraically transforms the expression for completeness as: $(X+3)^2 = X^2 + 6X + 9$

This would imply that: $S = (X + 3)^2 - 9$

Thus adding $9$ to both sides would align with the choice: $9 + S = (X + 3)^2$

Therefore, the correct statement that matches this manipulation is:

9+S equal to the smaller side plus 3 squared (the two squared).