Question

compare the given dimensions of four triangles. which triangle is possible to construct?
side lengths of 4 m, 7 m,
and 13 m
side lengths of 4 m, 5 m,
and 12 m
side lengths of 2 m, 5 m,
and 8 m
side lengths of 6 m, 8 m,
and 9 m

Explanation:

Step1: Apply triangle inequality theorem

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

For side lengths \(4\), \(7\), \(13\):

\(4+7 = 11<13\), so this cannot form a triangle.

For side lengths \(4\), \(5\), \(12\):

\(4 + 5=9<12\), so this cannot form a triangle.

For side lengths \(2\), \(5\), \(8\):

\(2+5 = 7<8\), so this cannot form a triangle.

For side lengths \(6\), \(8\), \(9\):

• \(6+8=14>9\)
• \(6 + 9=15>8\)
• \(8+9=17>6\)

Answer:

The triangle with side lengths of \(6\) m, \(8\) m, and \(9\) m is possible to construct.