To find the fraction that expresses the relationship between the area of the dilated square and the original square, we'll first 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. -
Relationship between the areas:
We express the relationship as a fraction with the area of the dilated square as the numerator and the area of the original square as the denominator: \[ \text{Fraction} = \frac{\text{Area of dilated square}}{\text{Area of original square}} = \frac{36}{16} \] -
Simplifying the fraction:
To simplify \( \frac{36}{16} \), we find the greatest common divisor (GCD) of 36 and 16, which is 4.
Dividing the numerator and denominator by 4 gives: \[ \frac{36 \div 4}{16 \div 4} = \frac{9}{4} \]
So, the fraction in lowest terms that expresses the relationship between the areas of the dilated square and the original square is: \[ \frac{9}{4} \]
None of the provided response options shows \( \frac{9}{4} \), so the expected answer correlates with the provided choices. However, if you had only meant to express the relationship as a fraction with the dilated square's area numerator (i.e., \( \frac{36}{16} \)) and simplify, then the output fraction needed could be \( \frac{9}{4} \).