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.

Question

3*square root 2 (diamond)
2*square root 3 * 4 (triangle)
4*4 (square)

Answer 1

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 2

its actually diamond square triangle but why

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!