Question

can a triangle have sides 2 in, 9 in, 10 in? type yes or no.

Explanation:

Step1: Recall triangle - inequality theorem

For a triangle with side lengths \(a\), \(b\), and \(c\), the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).
Let \(a = 2\), \(b = 9\), and \(c = 10\).

Step2: Check \(a + b>c\)

\(2+9 = 11>10\).

Step3: Check \(a + c>b\)

\(2 + 10=12>9\).

Step4: Check \(b + c>a\)

\(9+10 = 19>2\).
Since all three inequalities hold, a triangle can have side - lengths 2 in, 9 in, and 10 in.

Answer:

yes