To find the fraction that represents 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 = 4 units.
- Area = side × side = \( 4 \times 4 = 16 \) square units.
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Area of the dilated square:
- The side length of the dilated square = 6 units.
- Area = side × side = \( 6 \times 6 = 36 \) square units.
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Form the fraction to express the relationship:
- We want the fraction in the form (Area of the dilated square) / (Area of the original square).
- This gives us the fraction \( \frac{36}{16} \).
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Simplifying the fraction:
- \( \frac{36}{16} = \frac{9}{4} \) when simplified (by dividing both the numerator and denominator by 4).
The final result, in lowest terms, is \( \frac{9}{4} \). Since the numerator should express the area of the dilated square, the correct format of the answer would be \( \frac{36}{16} \) indicating area of dilated over area of original.
Thus, the answer is \( \frac{36}{16} \), which can also be noted as \( 9/4 \), but since the task is to express it as a fraction with 36 as the numerator, the most appropriate expression is simply \( \frac{36}{16} \).
If you were to be prompted to select from a list based on the simplifications, ensure you identify \( \frac{9}{4} \) as that is reflecting the area proportion correctly.
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