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
8 cm and 9 cm

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the known side be \(a = 13\) cm, and the other two sides be \(b\) and \(c\). We need to check \(b + c>a\), \(b + a>c\), and \(c + a>b\).

Step2: Check option 1 (7 cm and 2 cm)

If \(b = 7\) cm and \(c = 2\) cm, then \(b + c=7 + 2=9\) cm. Since \(9<13\), a triangle with side - lengths 7 cm, 2 cm, and 13 cm cannot be formed.

Step3: Check option 2 (8 cm and 9 cm)

If \(b = 8\) cm and \(c = 9\) cm, then \(b + c=8 + 9 = 17\) cm (\(17>13\)), \(b + a=8+13 = 21\) cm (\(21>9\)), and \(c + a=9 + 13=22\) cm (\(22>8\)). So, a triangle with side - lengths 8 cm, 9 cm, and 13 cm can be formed.

Answer:

8 cm and 9 cm