Question

Two sides of a triangle are of length $5cm$ and $1.5cm$. Which of the following cannot be the length of the third side of the triangle?

• A. 6.5 cm
• B. 4.3 cm
• C. 3.6 cm
• D. 4 cm

Answer 1

The correct option is A 6.5 cm

Given, the lengths of two sides of a triangle are $5cm$ and $1.5cm$, respectively.
Let sides $AB=5cm$ and $CA=1.5cm$ in $\Delta ABC$.
We know that sum of any two sides of a triangle is greater than the third side.
$\therefore$ $BC+CA>AB$ and $AB+CA>BC$
$\Rightarrow$ $BC+1.5>5$ and $5+1.5>BC$
$\Rightarrow$ $BC>5-1.5$ and $6.5>BC$
$\Rightarrow$ $BC>3.5$ and $BC<6.5$
Hence, the length of the third side cannot be $6.5cm$.