The sides of a triangle are in the ratio 4 : 6 : 8. The triangle is a/an:

obtuse-angled

If the sum of squares of the smaller sides is less than the square of the largest side, then it is an obtuse triangle.

Calculations

\( {4x }^{2 } \) + \( {6x }^{2 } \)  \(<\) \( {8x }^{2 } \)

⇒ \( {52x }^{2 } \)  \(<\) \( {64x }^{2 } \)

Therefore, the triangle is an obtuse triangle.