Question

If $a,b,c$ are the side lengths of a triangle $ABC$, match the following:

• A. Degenerate Triangle
• B. Scalene Triangle
• C. Isoceles Triangle
• D. Not a triangle

Answer 1

Triangle inequality states for any triangle, the sum of lengths of any two side is greater than the length of the third side.
Using the same condition, let's figure out the appropiate names:
A. $a=6;b=6;c=12$
Here, $a+b=6+6=12$ units which is equal to $c$
Hence, a degenerate triangle.
B. $a=6;b=7;c=3$
Here, the sum of any two sides is always greater than the third side.
Also, the side lengths are different for each side.
$\therefore$ It's a scalene triangle.
C. $a=10;b=5;c=4$
Here, $b+c=9<a$
$\therefore$ It's not forming a triangle.

D. $a=6;b=6;c=10$
Here, the sum of side lengths of any two sides is always greater than the third side.
Moreover $a=b$
$\therefore$ It's an isosceles triangle.