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

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

Option 2: \(2\) in, \(5\) in, \(6\) in

\(2+5>6\) (\(7>6\)), \(2 + 6>5\) (\(8>5\)), \(5+6>2\) (\(11>2\)).
\(3\) in, \(4\) in, \(7\) in
\(3 + 4=7\), which does not satisfy \(a + b>c\).

Option 3: \(2\) in, \(3\) in, \(4\) in

\(2+3>4\) (\(5>4\)), \(2 + 4>3\) (\(6>3\)), \(3+4>2\) (\(7>2\)).
\(5\) in, \(6\) in, \(7\) in
\(5+6>7\) (\(11>7\)), \(5 + 7>6\) (\(12>6\)), \(6+7>5\) (\(13>5\)).

Option 4: \(2\) in, \(3\) in, \(6\) in

\(2+3<6\) (\(5<6\)), which does not satisfy \(a + b>c\).

Answer:

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