Question

21 determine if the side lengths could form a triangle. 10 in, 10 in, 10 in

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let \(a = 10\), \(b = 10\), and \(c = 10\).

• Check \(a + b>c\): \(10+10>10\), which simplifies to \(20>10\) (True).
• Check \(a + c>b\): \(10 + 10>10\), which simplifies to \(20>10\) (True).
• Check \(b + c>a\): \(10+10>10\), which simplifies to \(20>10\) (True).

Answer:

Yes, the side - lengths \(10\) in, \(10\) in, \(10\) in can form a triangle.