Question

creating triangles from given side lengths
charla has six segments with which to make two triangles. the segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in.
which are possible side lengths of her two triangles?
2 in., 5 in., 6 in.
and 3 in., 4 in.,
7 in.
2 in., 4 in., 6 in.
and 3 in., 5 in.,
7 in.
2 in., 3 in., 6 in.
and 4 in., 5 in.,
7 in.
2 in., 3 in., 4 in.
and 5 in., 6 in.,
7 in.

Explanation:

Step1: Recall triangle inequality theorem

For a triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\)

Step2: Check each option

• Option 1: Triangles \(2\) in, \(5\) in, \(6\) in and \(3\) in, \(4\) in, \(7\) in
• For \(2\), \(5\), \(6\): \(2+5 = 7>6\), \(2 + 6=8>5\), \(5+6 = 11>2\)
• For \(3\), \(4\), \(7\): \(3+4=7\) (violates \(a + b>c\) as \(3 + 4

ot>7\))

• Option 2: Triangles \(2\) in, \(4\) in, \(6\) in and \(3\) in, \(5\) in, \(7\) in
• For \(2\), \(4\), \(6\): \(2+4=6\) (violates \(a + b>c\) as \(2 + 4

ot>6\))

• Option 3: Triangles \(2\) in, \(3\) in, \(6\) in and \(4\) in, \(5\) in, \(7\) in
• For \(2\), \(3\), \(6\): \(2+3 = 5<6\) (violates \(a + b>c\))
• Option 4: Triangles \(2\) in, \(3\) in, \(4\) in and \(5\) in, \(6\) in, \(7\) in
• For \(2\), \(3\), \(4\): \(2+3=5>4\), \(2 + 4=6>3\), \(3+4 = 7>2\)
• For \(5\), \(6\), \(7\): \(5+6=11>7\), \(5 + 7=12>6\), \(6+7 = 13>5\)

Answer:

\(2\) in, \(3\) in, \(4\) in and \(5\) in, \(6\) in, \(7\) in