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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, diamond, triangle
square, diamond, triangle

triangle, square, diamond
triangle, square, diamond

diamond, square, triangle
diamond, square, triangle

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

To determine the correct order of the hanging ornaments from tallest to shortest based on their heights, we analyze the given information.

1. Equilateral Triangle:

   • Height (bisecting line): $2\times \sqrt{3}$ inches

2. Rhombus:

   • Height (bisecting line): $3\times \sqrt{2}$ inches

3. Square:

   • Height: 4 inches

Now, we need to calculate the approximate values of the heights:

1. Equilateral Triangle: $$2\times \sqrt{3}\approx 2\times 1.732=3.464\text{ inches}$$

2. Rhombus: $$3\times \sqrt{2}\approx 3\times 1.414=4.242\text{ inches}$$

3. Square:

   • Height = 4 inches

Now we compare the heights:

• Triangle: 3.464 inches
• Rhombus: 4.242 inches
• Square: 4 inches

Ordering from tallest to shortest, we have:

1. Rhombus: 4.242 inches
2. Square: 4 inches
3. Triangle: 3.464 inches

Thus, the correct order from tallest to shortest is: diamond (rhombus), square, triangle.

So, the response is: diamond, square, triangle.