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 option 1 (\(a = 5\), \(b = 8\))

\(a + b=5 + 8=13\). But \(a + b\) should be greater than \(c\) (\(13\)). So \(5\) cm and \(8\) cm is not valid.

Step3: Check option 2 (\(a = 6\), \(b = 7\))

\(a + b=6+7 = 13\). But \(a + b\) should be greater than \(c\) (\(13\)). So \(6\) cm and \(7\) cm is not valid.

Step4: Check option 3 (\(a = 7\), \(b = 2\))

\(a + b=7 + 2=9<13\). So \(7\) cm and \(2\) cm is not valid.

Step5: Check option 4 (\(a = 8\), \(b = 9\))

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

Answer:

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