Question

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 greater than the length of the third side.
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 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:

To determine if three side lengths form a triangle, we use the triangle inequality theorem: the sum of any two sides must be greater than the third side.

• Check \(6 + 8\): \(6 + 8 = 14\), and \(14>10\).
• Check \(6 + 10\): \(6 + 10 = 16\), and \(16>8\).
• Check \(8 + 10\): \(8 + 10 = 18\), and \(18>6\).

Since the sum of any two sides is greater than the third, they form a triangle. The correct option is the one stating this.

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.