Question

first figure: a triangle with side lengths of 2, 6, and 9. second figure: a triangle with side lengths of 5, 7, and 8. if there is no triangle possible with the given side lengths, click on no triangle possible.

Explanation:

Step1: Check the first triangle

For a triangle with side lengths \(a = 2\), \(b = 6\), \(c = 9\).
We use the triangle - inequality theorem: \(a + b>c\), \(a + c>b\), \(b + c>a\).
\(a + b=2 + 6=8<9\).

Step2: Check the second triangle

For a triangle with side lengths \(a = 5\), \(b = 7\), \(c = 8\).
\(a + b=5+7 = 12>8\), \(a + c=5 + 8=13>7\), \(b + c=7 + 8=15>5\).

Answer:

First figure: No triangle possible. Second figure: A triangle can be formed.