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Question Number 185828 by normans last updated on 28/Jan/23

Commented by mr W last updated on 28/Jan/23

$${(x+y+z)}_{min}=\sqrt{\frac{a^2+b^2+c^2+4\sqrt{3}\mathrm{\Delta }}{2}}$$$$\mathrm{\Delta }=areaoftriangleABC$$$$\cos B=\frac{2^2+4^2-{\left(2\sqrt{3}\right)}^2}{2\times 2\times 4}=\frac{1}{2}$$$$\Rightarrow \sin B=\frac{\sqrt{3}}{2}$$$$\mathrm{\Delta }=\frac{2\times 4\times \sqrt{3}}{2\times 2}=2\sqrt{3}$$$${(x+y+z)}_{min}=\sqrt{\frac{2^2+4^2+{\left(2\sqrt{3}\right)}^2+4\sqrt{3}\times 2\sqrt{3}}{2}}$$$$=2\sqrt{7}$$

Commented by mr W last updated on 28/Jan/23

$$seeQ164174$$

Commented by normans last updated on 28/Jan/23

$$nicesir$$

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