Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

(B) {6,6,7}

Step-by-step explanation:

A criterion to determine if each triplet represents a triangle is the Law of Cosine, which states that:

Where , and are sides of the triangle and is the angle opposite to side . Now, let is clear the cosine function:

Cosine is a bounded function between -1 and 1, a triplet corresponds to a triangle if and only if result is located between upper and lower bounds. Now let is evaluate each triplet:

a) , ,

(Absurd)

The triplet does not represent a triangle.

b) , ,

(Reasonable)

The triplet represents a triangle.

c) , ,

(Absurd)

The triplet does not represent a triangle, but a straight line.

d) , ,

(Absurd)

The triplet does not represent a triangle, but a straight line.

Hence, the correct answer is B.

f

step-by-step explanation:

f