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? 7 cm and 2 cm 5 cm and 8 cm 6 cm and 7 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: \(a = 7\) cm, \(b = 2\) cm

\(a + b=7 + 2=9<13\). So, this is not a valid triangle.

• Option 2: \(a = 5\) cm, \(b = 8\) cm

\(a + b=5 + 8 = 13\). Since \(a + b
ot>c\), this is not a valid triangle.

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

\(a + b=6+7 = 13\). Since \(a + b
ot>c\), this is not a valid triangle.

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

\(a + b=8 + 9=17>13\), \(a + c=8+13 = 21>9\), \(b + c=9 + 13=22>8\). This satisfies the triangle - inequality theorem.

Answer:

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