If we have three sides of a,b,c and a is the longest side of the triangle, the following formula will define what type the triangle is.
Right triangle a² = b² + c²
Acute triangle a² < b² + c²
Obtuse triangle a² > b² + c²
Check each option
Option A
14² ... 10² + 8²
196 ... 100 + 64
196 > 164 (this is obtuse triangle)
Option B
15² ... 9² + 12²
225 ... 81 + 144
225 = 225 (this is right triangle)
Option C
17² ... 10² + 14²
289 ... 100 + 196
289 < 296 (this is acute triangle)
Option D
19² ... 12² + 15²
361 ... 144 + 225
361 < 369 (this is acute triangle)
The only answer is OPTION A
