Question

Chaz draws a square with sides equal to 4 units, then he dilates the square so the sides are equal to 6 units. Chaz writes a fraction in lowest terms to express the relationship between the area of the original square and the dilated square, with the numerator expressing the area of the dilated square. What is that fraction? (1 point) Responses 49 Start Fraction 4 over 9 End Fraction 214 2 Start Fraction 1 over 4 End Fraction 23 Start Fraction 2 over 3 End Fraction 1636

Answer 1

To find the relationship between the area of the original square and the dilated square, we need to calculate the area of both squares.

1. Area of the original square:

   • Side length = 4 units
   • Area = side length × side length = \(4 \times 4 = 16\) square units

2. Area of the dilated square:

   • Side length = 6 units
   • Area = side length × side length = \(6 \times 6 = 36\) square units

Now we express the relationship as a fraction, with the numerator as the area of the dilated square and the denominator as the area of the original square:

\[ \text{Fraction} = \frac{\text{Area of dilated square}}{\text{Area of original square}} = \frac{36}{16} \]

To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor (GCD), which is 4:

\[ \frac{36 \div 4}{16 \div 4} = \frac{9}{4} \]

Therefore, the fraction that expresses the relationship between the area of the original square and the dilated square is:

\[ \frac{9}{4} \]

In lowest terms, the answer is \(\boxed{\frac{9}{4}}\).