To find the relationship between the area of the original square and the dilated square, we first need to calculate the areas of both squares.
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Area of the original square (side length = 4 units): \[ \text{Area}_{\text{original}} = \text{side}^2 = 4^2 = 16 \text{ square units} \]
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Area of the dilated square (side length = 6 units): \[ \text{Area}_{\text{dilated}} = \text{side}^2 = 6^2 = 36 \text{ square units} \]
Next, we express the relationship between the area of the dilated square (numerator) and the area of the original square (denominator) as a fraction: \[ \text{Fraction} = \frac{\text{Area}{\text{dilated}}}{\text{Area}{\text{original}}} = \frac{36}{16} \]
Now, we simplify this fraction: \[ \frac{36}{16} = \frac{9}{4} \quad (\text{dividing both numerator and denominator by 4}) \]
Thus, the fraction that expresses the relationship between the area of the original square and the dilated square is: \[ \frac{9}{4} \]
However, since you are asked to express this in the form where the numerator is the area of the dilated square in relation to the original square, we write it as \( \frac{36}{16} \) directly, but reduced, it comes to \( \frac{9}{4} \).
This means that, among the options given, the relationship isn't exactly present.
However, if we re-express the fraction based on the reverse relationship (original to dilated), it becomes: \[ \frac{\text{Area (dilated)}}{\text{Area (original)}} = \frac{36}{16} \rightarrow \frac{9}{4} \text{ (In terms of the area of the dilated square to area of the original square)} \]
So all in all, the final answer represents \( \frac{9}{4} \) or the relationship expressed correctly based on your question.
out of the options, none seem to exactly fit this criteria, please consider restating the question or options.
1 answer