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: Recall 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 \(c = 13\) cm.

Step2: Check each option

• Option 1: \(a = 5\) cm, \(b = 8\) cm

\(a + b=5 + 8=13\) cm. But \(a + b\) should be \(>c\) (where \(c = 13\)). So \(5+8
ot>13\).

• Option 2: \(a = 6\) cm, \(b = 7\) cm

\(a + b=6 + 7 = 13\) cm. But \(a + b\) should be \(>c\) (where \(c = 13\)). So \(6 + 7
ot>13\).

• Option 3: \(a = 7\) cm, \(b = 2\) cm

\(a + b=7+2 = 9\) cm. Since \(9<13\) (\(a + b
ot>c\) where \(c = 13\)).

• Option 4: \(a = 8\) cm, \(b = 9\) cm

\(a + b=8 + 9=17\) cm (\(17>13\)), \(a + c=8+13 = 21>9\), \(b + c=9 + 13=22>8\).

Answer:

8 cm and 9 cm