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

$$\mathrm{If}2\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{are}\hat{\mathrm{i}}+2\hat{\mathrm{j}}\mathrm{and}$$$$\hat{\mathrm{i}}+\hat{\mathrm{k}},\mathrm{then}\mathrm{find}\mathrm{all}\mathrm{possible}\mathrm{third}\mathrm{side}?$$

Answered by MJS last updated on 01/Sep/18

$$\mathrm{any}\mathrm{triangle}:$$$$a+b>c$$$$a+c>b$$$$b+c>a$$$$$$$$\mathrm{this}\mathrm{case}:$$$$i+2j+i+k>c\Rightarrow c<2i+2j+k$$$$i+2j+c>i+k\Rightarrow c>k-2j$$$$i+k+c>i+2j\Rightarrow c>2j-k$$$$$$$$\Rightarrow \mathrm{case}1:k-2j<c<2i+2j+k\wedge 2j<k$$$$\mathrm{case}2:2j-k<c<2i+2j+k\wedge k<2j$$

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

$$\mathrm{ok}\mathrm{sir}\mathrm{thnks}.$$

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