Question

chang knows one side of a triangle is 13 cm. which set of two sides is possible for the lengths of the other two sides of this triangle? 5 cm and 8 cm 6 cm and 7 cm 7 cm and 2 cm 8 cm and 9 cm

Explanation:

Step1: Apply triangle inequality theorem

For a triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let the known side \(c = 13\) cm.

Step2: Check each option

• Option 1: \(a = 8\) cm, \(b=9\) cm

\(8 + 9=17>13\), \(8 + 13 = 21>9\), \(9+13=22>8\).

• Option 2: \(a = 7\) cm, \(b = 2\) cm

\(7+2=9<13\).

• Option 3: \(a = 6\) cm, \(b = 7\) cm

\(6 + 7=13\) (violates \(a + b>c\) as it should be \(>\) not \(=\)).

• Option 4: \(a = 5\) cm, \(b = 8\) cm

\(5+8 = 13\) (violates \(a + b>c\) as it should be \(>\) not \(=\)).

Answer:

\(8\) cm and \(9\) cm