Question

sides of a triangle quick check
determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm. (1 point)
they cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.
they cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
they will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
they will form a triangle because the sum of any two of the side lengths is less than the length of the third side.

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check side - length combinations

For sides \(a = 6\) cm, \(b = 8\) cm, and \(c = 10\) cm:

• \(a + b=6 + 8=14\gt10\)
• \(a + c=6+10 = 16\gt8\)
• \(b + c=8 + 10=18\gt6\)

Answer:

They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.