Answer:
Option (C)
Step-by-step explanation:
Given sides of a triangle are 2, [tex]\sqrt{12}[/tex] and [tex]\sqrt{19}[/tex].
Option (A).
If the triangle is a right triangle.
By Pythagoras theorem,
(Longest side)² = (Leg 1)² + (Leg 2)²
[tex](\sqrt{19})^2=2^2+(\sqrt{12})^2[/tex]
19 = 4 + 12
19 = 16
Not true.
Therefore, its not a right triangle.
Option (B).
If it is a triangle following conditions will be followed.
1). a + b > c
2). b + c > a
3). a + c > b
For the given sides of the triangle,
1). 2 + √12 > √19 [True]
2). 2 + √19 > √12 [True]
3). √12 + √19 > 2 [True]
Therefore, the given measures of the sides will form a triangle.
Option (C)
By Pythagorean inequality theorem,
If c² = a² + b² → Right triangle
If c² > a² + b² → Obtuse triangle
If c² < a² + b² → Acute triangle
Since, (√19)² > 2² + (√12)² → 19 > 4 + 12
Therefore, the given triangle is an Obtuse triangle.
Option (D).
Not true. It's an obtuse triangle.
