Math Problem Statement

Using the image provided, which of the following describes the side lengths of the triangle from least to greatest?

Using the image provided, which of the following describes the side lengths of the triangle from least to greatest?

Solution

The image provided shows an equilateral triangle where each internal angle is 60°. In an equilateral triangle, all sides are equal in length. Since the angles A=N=D=60\angle A = \angle N = \angle D = 60^\circ, the side lengths between the points AA, NN, and DD are also equal.

Thus, the side lengths of the triangle are all the same. So, there isn't a need to order them from least to greatest—they are all equal.

Would you like further details on equilateral triangles or have any related questions?

Here are five related questions:

  1. What is the general formula for the perimeter of an equilateral triangle?
  2. How do we calculate the height of an equilateral triangle given the side length?
  3. Can we find the area of this equilateral triangle if the side length is known?
  4. How would the triangle change if one angle was different from 60°?
  5. What is the relationship between the side lengths and angles in a non-equilateral triangle?

Tip: In any equilateral triangle, knowing just one side length gives you enough information to calculate the perimeter and the area.

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Math Problem Analysis

Mathematical Concepts

Geometry
Equilateral Triangle
Angles

Formulas

In an equilateral triangle, all sides are equal
Perimeter = 3 * side length
Area = (sqrt(3)/4) * side length^2

Theorems

Equilateral Triangle Theorem

Suitable Grade Level

Grades 6-8