Question

do the sides 6, 8, 9 form a triangle?
if so, classify the triangle as acute, obtuse, right or none.

Explanation:

Step1: Check triangle inequality

For three sides \(a\), \(b\), \(c\) (where \(c\) is the largest side), the triangle inequality states \(a + b>c\). Here, \(a = 6\), \(b = 8\), \(c = 9\). So, \(6+8 = 14>9\), \(6 + 9=15>8\), \(8 + 9 = 17>6\). So, they form a triangle.

Step2: Classify the triangle (using Pythagorean theorem extension)

For a triangle with sides \(a\), \(b\), \(c\) (\(c\) largest), if \(c^{2}a^{2}+b^{2}\), obtuse.
Calculate \(a^{2}+b^{2}=6^{2}+8^{2}=36 + 64 = 100\), \(c^{2}=9^{2}=81\). Since \(81<100\) (i.e., \(c^{2}

Answer:

Do the sides 6, 8, 9 form a triangle? Yes
If so, classify the triangle as acute, obtuse, right or none. Acute