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?

Question

(1 point)
Responses

214
2 Start Fraction 1 over 4 End Fraction

1636
16 over 36

49
Start Fraction 4 over 9 End Fraction

23

Answer 1

To find the fraction that expresses the relationship between the area of the original square and the dilated square, follow these steps:

1. Calculate the area of the original square.
   The original square has sides of length 4 units.
   Area = side length × side length = \(4 \times 4 = 16\) square units.

2. Calculate the area of the dilated square.
   The dilated square has sides of length 6 units.
   Area = side length × side length = \(6 \times 6 = 36\) square units.

3. Set up the fraction.
   The fraction representing the relationship between the area of the dilated square (numerator) and the area of the original square (denominator) is \( \frac{36}{16} \).

4. Reduce the fraction to lowest terms.
   To simplify \( \frac{36}{16} \), divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4.
   \( \frac{36 \div 4}{16 \div 4} = \frac{9}{4} \).

So, the fraction that expresses the relationship in lowest terms is \( \frac{9}{4} \).

None of the provided responses match \( \frac{9}{4} \). However, based on calculations, the answer would be

\( \frac{9}{4} \) (if this option were present).

But since it's not listed, please check if these fractions are incomplete or if something has occurred in the problem presentation. The closest one that could lead to that ratio (in the question list) does not appear directly within those fractions.