MCQ
In any $\triangle\text{ABC},\text{AB}+\text{BC}+\text{CA}$ is________________
  • A
    $\text{Less than}\frac{1}{3}\text{AB}$
  • B
    $\text{Equal to}\frac{1}{2}\text{AB}$
  • C
    $\text{Less than}\text{ AB}$
  • $\text{Greater than}\text{ 2AB}$

Answer

Correct option: D.
$\text{Greater than}\text{ 2AB}$

In any Triangle, the sum of any two sides is always greater than the
other side.in $\triangle\text{ABC},\text{AB}+\text{BC}>\text{CA}....\text{eqn(1)}$
$\text{BC + CA > AB}.....\text{eqn}(2)$
$\text{CA + AB > BC}...\text{eqn}(3)$ In equation $(2),$ adding $AB$ both side we
get, $\text{AB + BC + CA > 2AB}$

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