Use the image to answer the question.

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

diamond, square, triangle
diamond, square, triangle

square, diamond, triangle
square, diamond, triangle

square, triangle, diamond
square, triangle, diamond

triangle, square, diamond
triangle, square, diamond
Skip to navigation
page 19 of 19

Answer 1

To determine the order of the ornaments from tallest to shortest based on the given measurements, we need to evaluate the heights of each shape.

1. Triangle: The height is given as \( 2 \times \sqrt{3} \) inches.

   • Using a calculator, \( 2 \times \sqrt{3} \approx 2 \times 1.732 \approx 3.464 \) inches.

2. Rhombus: The height is given as \( 3 \times \sqrt{2} \) inches.

   • Using a calculator, \( 3 \times \sqrt{2} \approx 3 \times 1.414 \approx 4.242 \) inches.

3. Square: The height is given as 4 inches.

Now we have:

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

Ordering these heights from tallest to shortest:

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

Thus, the correct order is diamond, square, triangle.

Answer: diamond, square, triangle