Question

For the given side lengths, for which of the following a triangle can be formed:
A. $9,3,5$
B. $1,2,3$
C. $10,8,6$

• A. A. $9,3,5$
• B. B. $1,2,3$
• C. $10,8,6$
• D. None of these.

Answer 1

The correct option is C $10,8,6$

Triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.
Let's take the cases on by one.
A. $9,3,5$
Clearly $5+3=8<9$
$\therefore$ Not a triangle

B. $1,2,3$
Clearly $1+2=3$
$\therefore$ A degenerate triangle.

C. $10,8,6$
Here, sum of any two sides is greater than the length of the third side.
$\therefore$ A triangle.