Question

is it possible to draw triangle with 3.1 cm,1.9 cm and 5.1 cm as its sides . give reason​

Answer 1

Answer:

yes use herons formula to prove it

Answer 2

Given,

The lenght of the sides are $\[3.1{\rm{cm}},1.9{\rm{cm}}\,{\rm{and}}\,5.1\,{\rm{cm}}\]$respectively.

Solution,

In order to evaluate if a traingle is possible from the given length of sides apply Heron's formula.

Calculate the semi-perimerter,$\[s\]$.

$\[\begin{array}{l} \Rightarrow \frac{{3.1 + 1.9 + 5.1}}{2}\\ \Rightarrow \frac{{10.1}}{2}\\ \Rightarrow 5.05\end{array}\]$

Calculate the area of the triangle.

$\[\begin{array}{l} \Rightarrow \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \\ \Rightarrow \sqrt {5.05\left( {5.05 - 3.1} \right)\left( {5.05 - 1.9} \right)\left( {5.05 - 5.1} \right)} \\ \Rightarrow \sqrt {5.05 \times 1.95 \times 3.15 \times \left( { - 0.05} \right)} \\ \Rightarrow \sqrt { - 1.55} \end{array}\]$

Know that the area of the triangle cannot be a negative value.

Hence, it is not possible to draw a triangle having sides$\[3.1{\rm{cm}},1.9{\rm{cm}}\,{\rm{and}}\,5.1\,{\rm{cm}}{\rm{.}}\]$