Question

What type of triangle has these side lengths

Answer 1

Answer:

Option (C)

Step-by-step explanation:

Given sides of a triangle are 2, $\sqrt{12}$ and $\sqrt{19}$.

Option (A).

If the triangle is a right triangle.

By Pythagoras theorem,

(Longest side)² = (Leg 1)² + (Leg 2)²

$(\sqrt{19})^2=2^2+(\sqrt{12})^2$

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.