To find the fraction that expresses 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:
The side length of the original square is 4 units.
Area = side × side = \(4 \times 4 = 16\) square units. -
Area of the dilated square:
The side length of the dilated square is 6 units.
Area = side × side = \(6 \times 6 = 36\) square units.
Now, we express the relationship between the area of the dilated square (numerator) and the area of the original square (denominator):
\[ \text{Fraction} = \frac{\text{Area of the dilated square}}{\text{Area of the original square}} = \frac{36}{16} \]
Next, we simplify this fraction:
\[ \frac{36}{16} = \frac{9}{4} \]
Thus, the fraction representing the relationship between the area of the dilated square and the original square in lowest terms is:
\[ \frac{9}{4} \]
This fraction does not directly match any of the exact responses listed. However, the closest interpretation to express the area of the dilated square relative to the original square clearly indicates:
The answer is \(\frac{36}{16}\) which simplifies to \(\frac{9}{4}\).