Question

A company makes hanging ornaments in various shapes. The heights of the ornaments are shown. Using a calculator, order these ornaments from tallest to shortest.
3*square root 2 (diamond)
2*square root 3 * 4 (triangle)
4*4 (square)

Answer 1

its actually diamond square triangle but why

Answer 2

To order the heights of the ornaments from tallest to shortest, we need to calculate the actual numerical values of each expression.

1. **Diamond:**
\[
3 \sqrt{2}
\]
Calculating \( \sqrt{2} \) (approximately 1.414):
\[
3 \sqrt{2} \approx 3 \times 1.414 \approx 4.242
\]

2. **Triangle:**
\[
2 \sqrt{3} \times 4
\]
First calculate \( \sqrt{3} \) (approximately 1.732):
\[
2 \sqrt{3} \approx 2 \times 1.732 \approx 3.464
\]
Now multiply that by 4:
\[
3.464 \times 4 \approx 13.856
\]

3. **Square:**
\[
4 \times 4 = 16
\]

Now we can summarize the calculated heights:
- Diamond: \( \approx 4.242 \)
- Triangle: \( \approx 13.856 \)
- Square: \( 16 \)

Now we can order the heights from tallest to shortest:
1. Square: \( 16 \)
2. Triangle: \( 13.856 \)
3. Diamond: \( 4.242 \)

**Final order from tallest to shortest:**
1. Square
2. Triangle
3. Diamond

Answer 3

Let's double-check the calculations for clarity and make sure we arranged them correctly.

1. **Diamond:**
\[
3 \sqrt{2}
\]
Approximating \( \sqrt{2} \):
\[
\sqrt{2} \approx 1.414 \implies 3 \sqrt{2} \approx 3 \times 1.414 \approx 4.242
\]

2. **Square:**
\[
4 \times 4 = 16
\]

3. **Triangle:**
\[
2 \sqrt{3} \times 4
\]
Approximating \( \sqrt{3} \):
\[
\sqrt{3} \approx 1.732 \implies 2 \sqrt{3} \approx 2 \times 1.732 \approx 3.464
\]
Now multiply by 4:
\[
3.464 \times 4 \approx 13.856
\]

Now, let's list the calculated values:
- **Diamond:** \( \approx 4.242 \)
- **Square:** \( 16 \)
- **Triangle:** \( \approx 13.856 \)

If I had made a mistake in description, based on these calculations:
- **Tallest is Square:** \( 16 \)
- **Next is Triangle:** \( \approx 13.856 \)
- **Shortest is Diamond:** \( \approx 4.242 \)

Hence, if you say the order is Diamond, Square, Triangle, it seems there was a mix-up in interpretation. The calculated values do indicate:
1. Square (tallest)
2. Triangle (next)
3. Diamond (shortest)

It sounds like there may have been a miscommunication or misunderstanding. If there's a specific context or additional information that suggests the order was different, please share so we can further clarify!