Question

Is it possible to construct a triangle whose sides are $5.5\mathrm{cm}$, $4.5\mathrm{cm}$ and $10\mathrm{cm}$ ? If not , why ?

Answer 1

Let's assume triangle ABC such that $\mathrm{AB}=5.5\mathrm{cm},\mathrm{BC}=4.5\mathrm{cm},AC=10\mathrm{cm}$

In any triangle, the sum of any two sides is always greater than the third side,

like

$$\begin{gathered} \mathrm{AB}+\mathrm{BC}>A\mathrm{C} \\ \mathrm{BC}+A\mathrm{C}>\mathrm{AB} \\ \mathrm{AB}+A\mathrm{C}>\mathrm{BC} \end{gathered}$$

Here

$\mathrm{AB}+\mathrm{BC}=5.5+4.5=10$
And

$\mathrm{AC}=10$

So, $\mathrm{AB}+\mathrm{BC}=\mathrm{AC}$

Hence, the given triangle side lengths are not following the triangle property rule. So, with these sides the formation of a triangle is not possible.