To find the relationship between the areas of the original square and the dilated square, we need to calculate the areas of both squares:
-
Area of the original square:
- Side length = 4 units
- Area = side × side = \(4 \times 4 = 16\) square units
-
Area of the dilated square:
- Side length = 6 units
- Area = side × side = \(6 \times 6 = 36\) square units
Now we express the relationship as a fraction:
\[ \text{Fraction} = \frac{\text{Area of the dilated square}}{\text{Area of the original square}} = \frac{36}{16} \]
Next, we simplify the fraction:
\[ \frac{36}{16} = \frac{36 \div 4}{16 \div 4} = \frac{9}{4} \]
Thus, the fraction representing the relationship between the area of the dilated square and the original square in lowest terms is:
\(\frac{9}{4}\)
However, this does not match any options in your list. Please verify whether any option corresponds to \(\frac{9}{4}\) in lowest terms. Based on the provided responses, it seems that none of the options you provided match this result.
But among the responses listed, the correct answer appears to be missing, so the correct reduced fraction is:
\(\frac{9}{4}\) (which is not in the provided responses).