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Question Number 216164 by BaliramKumar last updated on 29/Jan/25

Answered by AntonCWX last updated on 29/Jan/25

$$Thesmallestdistancebetweentwosidesis2-1=1$$$$Thesumofthreesidesis1+2+4=7$$$$Letthefourthsidebed$$$$1<d<7$$$$possiblevalues:2,3,4,5,6$$$$C\left(5\right)$$

Answered by Wuji last updated on 29/Jan/25

$$\mathrm{a}=1,\mathrm{b}=2,\mathrm{c}=4$$$$1+2+4>\mathrm{d}$$$$\Rightarrow 7>\mathrm{d}$$$$1+2+\mathrm{d}>4\Rightarrow \mathrm{d}>1$$$$1+4+\mathrm{d}>2\Rightarrow \mathrm{d}>-3$$$$2+4+\mathrm{d}>1\Rightarrow \mathrm{d}>-5$$$$\mathrm{combing}\mathrm{the}\mathrm{inequalities}$$$$1<\mathrm{d}<7$$$$\mathrm{d}\in \mathbb{N}$$$$2,3,4,5,6$$$$5\mathrm{possible}\mathrm{integer}\mathrm{lengths}$$$$\mathrm{for}\mathrm{the}\mathrm{fourth}\mathrm{side}$$$$$$

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