Question

What type of triangle has side lengths 12, 13, and 2√3?

Answer 1

The triangle is an obtuse scalene triangle

Explanation:

we know that

if
`c^(2)=a^(2)+b^(2)` --------> is a right triangle

if
`c^(2)>a^(2)+b^(2)` --------> is an obtuse triangle

if
`c^(2)<a^(2)+b^(2)` --------> is an acute triangle

where

c is the greater side

we have

`c=13\ units`

`a=12\ units`

`b=2√(3)\ units`

so

`c^(2)=13^(2)=169`

`a^(2)+b^(2)=12^(2)+(2√(3))^(2)=156`

so

`c^(2)>a^(2)+b^(2)` -------> is an obtuse triangle

Remember that

The given triangle has three different length side

so

Is a scalene triangle

therefore

The triangle is an obtuse scalene triangle