Tag: triangle inequality related to lines and triangles

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Questions Related to triangle inequality related to lines and triangles

Multiple choice 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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
Multiple choice 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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.