Question

Which comparison about the shapes is true?

6 triangles and 2 rectangles.
For every 2 rectangles there are 8 triangles.
For every 6 triangles there are 8 rectangles.
For every 2 rectangles there are 4 triangles.
For every 6 triangles there are 2 rectangles.

Answer 1

To analyze the relationships between the numbers of triangles and rectangles, we can convert the statements into mathematical proportions.

1. **Original Count**: We have 6 triangles and 2 rectangles.
2. **Ratios**:
- The ratio of triangles to rectangles in the original count is 6 triangles : 2 rectangles.

Let's evaluate each statement:

1. **For every 2 rectangles there are 8 triangles.**
- If there are 2 rectangles, according to the original ratio, there would be \( \frac{6}{2} \times 2 = 6 \) triangles, not 8. **False.**

2. **For every 6 triangles there are 8 rectangles.**
- If there are 6 triangles, according to the original ratio, there are \( \frac{2}{6} \times 6 = 2 \) rectangles, not 8. **False.**

3. **For every 2 rectangles there are 4 triangles.**
- If there are 2 rectangles, according to the original ratio, there are \( \frac{6}{2} \times 2 = 6 \) triangles, not 4. **False.**

4. **For every 6 triangles there are 2 rectangles.**
- This matches the original ratio. For every 6 triangles, there indeed are 2 rectangles as per the original count. **True.**

5. **For every 6 triangles there are 2 rectangles.**
- This statement is the same as the one above and is also **True.**

The only true statement about the comparison of the shapes is: **For every 6 triangles, there are 2 rectangles.**