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 1636 16 over 36 214 2 Start Fraction 1 over 4 End Fraction 49 Start Fraction 4 over 9 End Fraction 23
Select One

Answer 1

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

1. **Area of the original square**:
The original square has a side length of 4 units. The area \(A_1\) is calculated as follows:
\[
A_1 = \text{side}^2 = 4^2 = 16 \text{ square units}
\]

2. **Area of the dilated square**:
The dilated square has a side length of 6 units. The area \(A_2\) is calculated as follows:
\[
A_2 = \text{side}^2 = 6^2 = 36 \text{ square units}
\]

3. **Fraction to express the relationship**:
We need to express the relationship by forming a fraction where the numerator is the area of the dilated square and the denominator is the area of the original square:
\[
\text{Fraction} = \frac{A_2}{A_1} = \frac{36}{16}
\]

4. **Simplifying the fraction**:
We can simplify \(\frac{36}{16}\):
\[
\frac{36}{16} = \frac{9}{4}
\]

The fraction expressing the relationship between the areas in lowest terms is:
\[
\frac{9}{4}
\]

Now, let’s express it in the form of the possible answers provided:

- \(16/36\) is equivalent to \(\frac{4}{9}\) (not in lowest terms).
- \(2\) is a whole number.
- \(\frac{1}{4}\) does not reflect the areas accurately.
- \(\frac{4}{9}\) is also not correct based on our calculations.

Therefore, since \(\frac{9}{4}\) isn't one of the exact options, the closest relationship involving both areas is given as:
\[
\frac{36}{16}
\]
So the best choice based on the incorrect options but aligning with our simplification would be:
- \(16/36\) (this simplifies to \(\frac{4}{9}\), which doesn't match but reflects a part of the area change).

The proper fraction representing the area comparison is:
\(\frac{9}{4}\) but none of the options match directly with that.