Try to construct a triangle with $5$ cm, $8$ cm and $1$ cm. Is it possible or not? Why? Give your justification?

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Solution

$\begin{matrix} A B = 5 c m B C = 8 c m C A = 1 c m I f t r i a n g l e p o s s i b l e, A B + B C > C A B C + C A > A B C A + A B > B C b u t h e r e C A + A B > B C [∵ n o t f o l l o w i n g r u l e s] 1 + 5 > 8 [∵ n o t f o l l o w i n g t r i a n g l e r u l e s f o r f e r m a t i o n] ∵ t r i a n g l e n o t p o s s i b l e h e r e . \end{matrix}$

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