Question

Which set of three segments can form a triangle?

7, 12, 5

6, 4, 11

13, 6, 6

8, 2, 8

Answer 1

By the Triangle Inequality, in order for three line segments to make a triangle, the sum of the lengths of any two line segments must exceed the length of the third line segment.

So, we have:
(a) 7 + 12 > 5, 7 + 5 = 12 ==> 7, 12, and 5 does NOT form a triangle
(b) 6 + 4 < 11 ==> 6, 4, and 11 does NOT form a triangle
(c) 13 + 6 > 6, 6 + 6 < 13 ==> 13, 6, and 6 does NOT form a triangle
(d) 8 + 2 > 8, 2 + 8 > 8, and 8 + 8 > 2 ==> 8, 2, and 8 DOES form a triangle.

Therefore, the answer is (d) 8, 2, 8.

I hope this helps

Answer 2

Thank you! Very easy to understand. :)