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Question

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.

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

square, triangle, diamond
square, triangle, diamond

triangle, square, diamond
triangle, square, diamond

diamond, square, triangle
diamond, square, triangle

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

To compare the heights of the ornaments based on the given measurements:

1. Square: The height is labeled as 4 inches.

2. Triangle: The height is labeled as \( 2 \times \sqrt{3} \) inches. Approximating \( \sqrt{3} \) (approximately 1.732), the height of the triangle is: \[ 2 \times \sqrt{3} \approx 2 \times 1.732 = 3.464 \text{ inches} \]

3. Rhombus (Diamond): The height is labeled as \( 3 \times \sqrt{2} \) inches. Approximating \( \sqrt{2} \) (approximately 1.414), the height of the rhombus is: \[ 3 \times \sqrt{2} \approx 3 \times 1.414 = 4.242 \text{ inches} \]

Now, comparing the heights:

• Height of the square: 4 inches
• Height of the triangle: approximately 3.464 inches
• Height of the rhombus: approximately 4.242 inches

Ordering these from tallest to shortest:

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

So, the correct order from tallest to shortest is: diamond, square, triangle.

Therefore, the answer is: diamond, square, triangle.