Question

select the 2 answers below that show three lengths that will make a triangle. 5,1,4 12,13,21 7,2,4 4,4,4 15,20,35

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for three side lengths \(a\), \(b\), \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

For \(5,1,4\):

\(1 + 4=5\), which does not satisfy \(a + b>c\) (since \(1 + 4
ot>5\)).

For \(12,13,21\):

• \(12+13 = 25>21\)
• \(12 + 21=33>13\)
• \(13+21 = 34>12\)

For \(7,2,4\):

\(2+4 = 6<7\), which does not satisfy \(a + b>c\).

For \(4,4,4\):

• \(4+4=8>4\)
• \(4 + 4=8>4\)
• \(4+4 = 8>4\)

For \(15,20,35\):

\(15+20=35\), which does not satisfy \(a + b>c\) (since \(15 + 20
ot>35\)).

Answer:

12,13,21 and 4,4,4