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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

diamond, square, triangle
diamond, square, triangle
triangle, square, diamond
triangle, square, diamond
square, triangle, diamond
square, triangle, diamond
square, diamond, triangle

1 answer

To determine the order of the heights of the ornaments (the triangle, rhombus, and square), we need to calculate the heights based on the information provided.

  1. Equilateral Triangle:

    • The base = 4 inches
    • The height (bisecting line) = \(2 \sqrt{3}\) inches

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

  2. Rhombus:

    • Side length = 3 inches
    • The height (bisecting line) = \(3 \sqrt{2}\) inches

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

  3. Square:

    • Side length = 4 inches
    • The height (bisecting line) = 4 inches

Now, comparing the calculated heights:

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

Ordering from tallest to shortest:

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

Thus, the order is: rhombus, square, triangle.

None of the provided responses match that order exactly, but if "diamond" represents the rhombus, then the correct response is:

diamond, square, triangle.