2. A triangle has sides \( 4,6 \sqrt{5}, 14 \). Classify the triangle by its sides. (Must show work for credit!)
a. Acute triangle
b. Obtuse triangle
c. Right triangle
d. The sides lengths cannot form a triangle
Answer
3. Conclude the triangle type: The triangle is a right triangle, because the square of the largest side is equal to the sum of the squares of the other two sides
Step 1 ：1. Calculate the square of each side: \(4^2 = 16\), \((6\sqrt{5})^2 = 180\), \(14^2 = 196\)
Step 2 ：2. Check if the sum of the squares of the two smallest sides equals the square of the largest side: \(16 + 180 = 196\)
Step 3 ：3. Conclude the triangle type: The triangle is a right triangle, because the square of the largest side is equal to the sum of the squares of the other two sides
