Question

Given the information, find all possible lengths of the three sides of a triangle. Which of the following equations describes one of the sides of the triangle?

A) a²=b²+c²
B) a+b>c
C) a−bD) a⋅b=c

Answer 1

The proper relation describing a side of the triangle from the options provided is option B, a+b>c, which is the Triangle Inequality Theorem. Options A resembles the Pythagorean theorem incorrectly stated, and options C and D do not generally apply to triangles.

Step-by-step explanation:

The question concerns the properties of a triangle's sides and their relationship to each other. Among the given options, option B, a+b>c, describes a fundamental property of triangles known as the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. On the other hand, option A, a²=b²+c², is an incorrect representation of the Pythagorean theorem, which is actually a² + b² = c² and only applies to right-angled triangles where c represents the hypotenuse. Option C is incomplete and does not represent the property of a triangle's side. Lastly, option D, a·b=c, does not generally apply to the sides of a triangle unless in specific cases of geometric figures like rectangles or squares when discussing area.