3 shapes are shown side by side: an equilateral triangle, a rhombus, and a square. Each has a vertical line that bisects it. Each has a hook-like shape extending from the top. Measurements labels are included for the bisecting line and an exterior face. The base of the triangle is labeled 4 inches and the bisecting line is labeled 2 times start root 3 end root inches. The side of the rhombus is labeled 3 inches and the bisecting line is labeled 3 times starts root 2 end root inches. The side of the square is labeled 4 inches and the bisecting line is labeled 4 inches.

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.

(1 point)
Responses

diamond, square, triangle
diamond, square, triangle

square, triangle, diamond
square, triangle, diamond

square, diamond, triangle
square, diamond, triangle

triangle, square, diamond
triangle, square, diamond
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Answer 1

To find the heights of the ornaments, we need to compare the lengths of the vertical bisecting lines for each shape:

1. Equilateral Triangle:

   • Bisecting line: \( 2 \sqrt{3} \) inches

2. Rhombus (Diamond):

   • Bisecting line: \( 3 \sqrt{2} \) inches

3. Square:

   • Bisecting line: 4 inches

Next, we will calculate the approximate values of these heights using a calculator:

1. Equilateral Triangle:

   • \( 2 \sqrt{3} \approx 2 \times 1.732 \approx 3.464 \) inches

2. Rhombus (Diamond):

   • \( 3 \sqrt{2} \approx 3 \times 1.414 \approx 4.242 \) inches

3. Square:

   • \( 4 \) inches (exact value)

Now, we can compare the heights:

• Triangle: \( 3.464 \) inches
• Diamond (Rhombus): \( 4.242 \) inches
• Square: \( 4 \) inches

Ordering these heights from tallest to shortest:

1. Diamond (4.242 inches)
2. Square (4 inches)
3. Triangle (3.464 inches)

Therefore, the correct response, ordering the ornaments from tallest to shortest, is:

diamond, square, triangle.

Answer 2

Your sure that's right?

Answer 3

Let's confirm the calculations clearly step by step for each shape's height:

1. Equilateral Triangle:

   • The height given is \( 2\sqrt{3} \).
   • Calculate \( 2 \sqrt{3} \): \[ \sqrt{3} \approx 1.732 \implies 2 \times 1.732 \approx 3.464 \text{ inches} \]

2. Rhombus (Diamond):

   • The height given is \( 3\sqrt{2} \).
   • Calculate \( 3 \sqrt{2} \): \[ \sqrt{2} \approx 1.414 \implies 3 \times 1.414 \approx 4.242 \text{ inches} \]

3. Square:

   • The height is \( 4 \) inches (given directly).

Now we compare the calculated heights:

• Triangle: \( 3.464 \) inches
• Diamond (Rhombus): \( 4.242 \) inches
• Square: \( 4 \) inches

Final Comparison:

• Tallest: Diamond (4.242 inches)
• Second Tallest: Square (4 inches)
• Shortest: Triangle (3.464 inches)

So, when we order them from tallest to shortest, the correct order indeed is:

diamond, square, triangle.

Thank you for your patience, and the calculation confirms that the order is correct.