Tag: sum of the lengths of two sides of a triangle

Questions Related to sum of the lengths of two sides of a triangle

O is a point that lies in the interior of $\Delta ABC$. Then $2(OA - OB -OC) > \text{Perimeter}\ of\ \Delta ABC$.

maths construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

  1. True

  2. False

Show answer
Correct Option: B
Explanation:
From the $\triangle ABC,$ by triangle inequality,
$ OA+OB>AB$ ....... $(i)$
$ OB+OC>BC$ ........ $(ii)$
$ OA+OC>AC$ ........ $(iii)$
By adding $(i),(ii)$ and $(iii)$
$ 2(OA+OB+OC)>AB+BC+AC$
$ \therefore 2(OA+OB+OC)>\text{Perimeter of triangle } ABC$
Hence, the statement is false.

Sum of the length of any two sides of a triangle is always greater than the length of third side.

maths construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

  1. True

  2. False

Show answer
Correct Option: A
$\dfrac{\sin 2x}{2\cos x}=\tan x \ \ ?$
maths construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

  1. True

  2. False

Show answer
Correct Option: A
Explanation:
LHS

$\dfrac{\sin 2x}{2\cos x}$

$\dfrac{2\sin x \cos x}{2\cos x}$

$\implies \dfrac{\sin x}{\cos x}$

$\implies \tan x $

Hence proved.