To find the relationship between the areas of the original square and the dilated square, we first calculate the areas of each square.
-
Original Square:
- Side length = 4 units
- Area = side length × side length = \(4 \times 4 = 16\) square units
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Dilated Square:
- Side length = 6 units
- Area = side length × side length = \(6 \times 6 = 36\) square units
Next, we express the relationship between the area of the dilated square and the area of the original square as a fraction: \[ \text{Fraction} = \frac{\text{Area of dilated square}}{\text{Area of original square}} = \frac{36}{16} \]
Now, we simplify this fraction: \[ \frac{36}{16} = \frac{9}{4} \quad (\text{after dividing both the numerator and denominator by 4}) \]
Thus, the fraction in lowest terms that expresses the relationship between the areas is: \[ \frac{9}{4} \]
Given the options presented, \(\frac{9}{4}\) is not listed among them, but this is the correct answer based on the calculations. If we need to match the form of the answer options, we take the existing areas and find their relationship correctly.
However, since the question specifically asks for the fraction as per the given instructions and options, the answer derived from the options needs to be correct within that context. Please double-check the problem context or options provided in case there's a mismatch. However, based on the direct calculation, the final answer is:
\(\frac{9}{4}\) (if presented as an equivalent option in the provided answers, but not listed).