Question

Is it possible to construct a triangle with lengths of its side 2cm,3cm,and 6cm. Give reason for your answer.

Answer 1

Heya ...!

As We Know Sum Of Two Sides Of A Triangle Must Be Greater Than The Third Side .

The Given Measurements Are 2cm , 3cm And 6cm .

2+3= 5 cm

Here The Sum Of The Two Sides Is Less Than Third Side .

Hence A Triangle Cannot Be Constructed .

Answer 2

$\underline{\mathsf{Answer}}$

According to the theorem we know that the third side of the triangle is smaller than the sum of other 2 sides of the triangle.                                                

Example :- Sides of the triangle ( 2, 3, 4 )

2 + 3 = 5

5 > 4 ∴ The triangle can be constructed

$\underline{\underline{\mathsf{Solution}}}$

$\mathsf{Sides\:of\: the \: triangle = 2 cm, 3 cm, 6 cm} \\ \\ \mathsf{According\: to \:the \:theoram\: a + b > c} \\ \\ \implies\mathsf{ 2+3 = 5 } \\\\ \implies\mathsf{5 < 6} \\\\ \mathsf{The\:sum\:of\:the\:two\:sides\:of\:the\:triangle\:is\:smaller\:then\:the\:3rd\:side} \\\\\boxed{\mathsf{This\: proves\: that\:the\: it's\: not\: possible\: to\: construct\: a\: triangle}}$