If-2-sides-of-a-triangle-are-i-2j-and-i-k-then-find-all-possible-third-side-

Question Number 42711 by rahul 19 last updated on 01/Sep/18

If 2 sides of a triangle are \hat{i} + 2 \hat{j} and

\hat{i} + \hat{k}, then find all possible third side ?

Answered by MJS last updated on 01/Sep/18

any triangle :

a + b > c

a + c > b

b + c > a

this case :

i + 2 j + i + k > c \Rightarrow c < 2 i + 2 j + k

i + 2 j + c > i + k \Rightarrow c > k - 2 j

i + k + c > i + 2 j \Rightarrow c > 2 j - k

\Rightarrow case 1 : k - 2 j < c < 2 i + 2 j + k \land 2 j < k

case 2 : 2 j - k < c < 2 i + 2 j + k \land k < 2 j

Commented by rahul 19 last updated on 02/Sep/18

ok sir thnks .