Question

Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning. Question 11 options: A) Yes, because the sum of any two side lengths is greater than the third side length. B) No, because 4 + 8 is greater than 10. C) Yes, because the sum of all three side lengths is greater than 20. D) No, because the third side length is greater than the sum of the other two side lengths.

Answer 1

A) Yes, because the sum of any two side lengths is greater than the third side length.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 4 + 8 = 12, which is greater than 10, and the other two combinations (4 + 10 and 8 + 10) also satisfy this rule. Therefore, the given side lengths do form a triangle.

Explanation: