Answer:
The triangle is an obtuse scalene triangle
Step-by-step explanation:
we know that
if [tex]c^{2}=a^{2}+b^{2}[/tex] --------> is a right triangle
if [tex]c^{2}>a^{2}+b^{2}[/tex] --------> is an obtuse triangle
if [tex]c^{2}<a^{2}+b^{2}[/tex] --------> is an acute triangle
where
c is the greater side
we have
[tex]c=13\ units[/tex]
[tex]a=12\ units[/tex]
[tex]b=2\sqrt{3}\ units[/tex]
so
[tex]c^{2}=13^{2}=169[/tex]
[tex]a^{2}+b^{2}=12^{2}+(2\sqrt{3})^{2}=156[/tex]
so
[tex]c^{2}>a^{2}+b^{2}[/tex] -------> 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
