Question

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

Answer 1

Is an scalene obtuse triangle

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=√(19)\ units`

`a=2\ units`

`b=√(12)\ units`

substitute

`c^(2)=(√(19))^(2)=19`

`a^(2)+b^(2)=(2)^(2)+(√(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