To determine which set of side lengths will form a triangle, we can use the triangle inequality theorem. This theorem states that for any three lengths \(a\), \(b\), and \(c\) to form a triangle, the following must be true:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
Now let's apply the theorem to each set of lengths:
-
50, 30, 80
- \(50 + 30 = 80 \not> 80\) (fails)
-
50, 60, 26
- \(50 + 60 = 110 > 26\) (true)
- \(50 + 26 = 76 > 60\) (true)
- \(60 + 26 = 86 > 50\) (true)
- (valid triangle)
-
60, 26, 33
- \(60 + 26 = 86 > 33\) (true)
- \(60 + 33 = 93 > 26\) (true)
- \(26 + 33 = 59 \not> 60\) (fails)
-
26, 12, 12
- \(26 + 12 = 38 > 12\) (true)
- \(26 + 12 = 38 > 12\) (true)
- \(12 + 12 = 24 \not> 26\) (fails)
From these evaluations, the set of side lengths that will form a triangle is:
50, 60, 26.
1 answer