Question

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., 3 in., 6 in. and 4 in., 5 in., 7 in.
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
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.

Explanation:

Step1: Check triangle inequality for each option

The triangle inequality states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\).

• Option 1: \(2\) in, \(3\) in, \(6\) in and \(4\) in, \(5\) in, \(7\) in
• For \(2\), \(3\), \(6\): \(2+3 = 5<6\), so this is not a triangle.
• Option 2: \(2\) 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 \(5\), \(6\), \(7\): \(5+6 = 11>7\), \(5 + 7=12>6\), \(6+7 = 13>5\)
• Option 3: \(2\) in, \(5\) in, \(6\) in and \(3\) in, \(4\) in, \(7\) in
• For \(3\), \(4\), \(7\): \(3+4=7\), not \(>7\), so this is not a triangle.
• Option 4: \(2\) in, \(4\) in, \(6\) in and \(3\) in, \(5\) in, \(7\) in
• For \(2\), \(4\), \(6\): \(2+4=6\), not \(>6\), so this is not a triangle.

Answer:

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