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Question Number 172062 by cortano1 last updated on 23/Jun/22

Answered by kapoorshah last updated on 23/Jun/22

$$s=\frac{10+14+16}{2}$$$$=20$$$$$$$$r=\sqrt{\frac{(20-10)(20-14)(20-16)}{20}}$$$$=2\sqrt{3}$$$$$$$$a+b=16$$$$b+c=10$$$$c+a=14$$$$$$$$\Rightarrow a=10,b=6,c=4$$$$$$$$x=\sqrt{{10}^2+{\left(2\sqrt{3}\right)}^2}$$$$=4\sqrt{7}$$$$$$$$y=\sqrt{4^2+{\left(2\sqrt{3}\right)}^2}$$$$=2\sqrt{7}$$$$$$$$z=\sqrt{6^2+{\left(2\sqrt{3}\right)}^2}$$$$=4\sqrt{3}$$$$$$$$x+y+z=6\sqrt{7}+4\sqrt{3}$$$$$$$$$$$$$$$$$$$$$$

Commented by kapoorshah last updated on 23/Jun/22

Commented by mr W last updated on 23/Jun/22

$$verynice!$$

Commented by Tawa11 last updated on 25/Jun/22

$$\mathrm{Great}\mathrm{sir}$$

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