Question

teacher:stirewalt class:1st period math 2 spring 2025 lee4tvsp student belcher, cash can a triangle have sides 2 in, 9 in, 10 in? type yes or no.

Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, 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 first inequality

\(a + b=2 + 9=11>10\) (i.e., \(a + b>c\)).

Step3: Check second inequality

\(a + c=2+10 = 12>9\) (i.e., \(a + c>b\)).

Step4: Check third inequality

\(b + c=9 + 10=19>2\) (i.e., \(b + c>a\)).
Since all three inequalities hold, a triangle can have sides 2 in, 9 in, and 10 in.

Answer:

yes