### Triangle Classification ProblemA triangle with side lengths \(2\), \(4\sqrt{6}\), and \(10\) is what type of triangle?**Options**:a) Acute b) Right c) There is not enough information to determine the answer. d) Obtuse To solve this, we need to apply the triangle inequality theorem and Pythagorean theorem.**Triangle Inequality Theorem**: The sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. Check:- \(2 + 4\sqrt{6} > 10\)- \(2 + 10 > 4\sqrt{6}\)- \(4\sqrt{6} + 10 > 2\)**Pythagorean Theorem for Right Triangles**: To determine if the triangle is right, check if \(a^2 + b^2 = c^2\), where \(c\) is the longest side.**Comparisons for Acuteness or Obtuseness**:- If \(a^2 + b^2 > c^2\), the triangle is acute.- If \(a^2 + b^2 < c^2\), the triangle is obtuse.You can verify these conditions to determine the correct type of triangle.

Name: ### Triangle Classification ProblemA triangle with side lengths \(2\)
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: ### Triangle Classification ProblemA triangle with side lengths \(2\), \(4\sqrt{6}\), and \(10\) is what type of triangle?**Options**:a) Acute b) Right c) There is not enough information to determine the answer. d) Obtuse To solve this, we need