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

Explanation:

Step1: Check triangle inequality for each option

Triangle inequality: \(a + b>c\), \(a + c>b\), \(b + c>a\) for side lengths \(a\), \(b\), \(c\) of a triangle.

Option 1: \(2\) in., \(4\) in., \(6\) in. and \(3\) in., \(5\) in., \(7\) in.

For \(2\), \(4\), \(6\): \(2 + 4=6\), does not satisfy \(a + b>c\).

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

For \(2\), \(3\), \(4\): \(2+3 > 4\), \(2 + 4>3\), \(3+4>2\).
For \(5\), \(6\), \(7\): \(5 + 6>7\), \(5+7>6\), \(6 + 7>5\).

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

For \(3\), \(4\), \(7\): \(3+4 = 7\), does not satisfy \(a + b>c\).

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

For \(2\), \(3\), \(6\): \(2+3<6\), does not satisfy \(a + b>c\).

Answer:

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