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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

triangle, square, diamond
triangle, square, diamond

diamond, square, triangle
diamond, square, triangle

square, triangle, diamond
square, triangle, diamond

square, diamond, triangle
square, diamond, triangle

Answer 1

To determine the heights of the ornaments based on the provided information:

1. Equilateral Triangle:

   • Base = 4 inches
   • Height (bisecting line) = \( 2\sqrt{3} \) inches
   • Calculate: \( 2\sqrt{3} \approx 3.46 \) inches

2. Rhombus (Diamond):

   • Side = 3 inches
   • Height (bisecting line) = \( 3\sqrt{2} \) inches
   • Calculate: \( 3\sqrt{2} \approx 4.24 \) inches

3. Square:

   • Side = 4 inches
   • Height (bisecting line) = 4 inches

Now, let’s order these heights:

• Rhombus: approximately 4.24 inches (tallest)
• Square: 4 inches (second)
• Triangle: approximately 3.46 inches (shortest)

Therefore, when ordered from tallest to shortest, the correct sequence is:

diamond, square, triangle

So the answer is: diamond, square, triangle