Question

What type of triangle has side lengths 2, √12, and √19?

Answer 1

Answer:

Is an scalene obtuse triangle

Step-by-step explanation:

step 1

Find the type of triangle by the measure of the interior angles

we know that

If applying the Pythagoras Theorem

$c^{2}=a^{2}+b^{2}$ ----> we have a right triangle

$c^{2} > a^{2}+b^{2}$ ----> we have an obtuse triangle

$c^{2}< a^{2}+b^{2}$ ----> we have an acute triangle

where

c is the greater side

we have

$c=\sqrt{19}\ units$

$a=2\ units$

$b=\sqrt{12}\ units$

substitute

$c^{2}=(\sqrt{19})^{2}=19$

$a^{2}+b^{2}=(2)^{2}+(\sqrt{12})^{2}=16$

so

$19 > 16$ -----> $c^{2} > a^{2}+b^{2}$

we have an obtuse triangle

step 2

Find the type of triangle by the measure of the sides

we have that

The measure of its three sides is different

therefore

Is an scalene triangle