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Question Number 177128 by cortano1 last updated on 01/Oct/22

Commented by cortano1 last updated on 01/Oct/22

$$\mathrm{all}\mathrm{angles}=120°.\mathrm{Find}\mathrm{the}\mathrm{perimeter}$$

Answered by mr W last updated on 01/Oct/22

Commented by cortano1 last updated on 01/Oct/22

$$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{formula}\mathrm{sir}?$$

Commented by mr W last updated on 02/Oct/22

$$6+4=b+9\Rightarrow b=1$$$$a+b=4+8\Rightarrow a+b=12\Rightarrow a=11$$$$perimeter=6+4+8+9+a+b=39✓$$

Commented by Rasheed.Sindhi last updated on 02/Oct/22

$$\mathcal{E}xcellent\mathit{s}\mathit{i}\mathit{r}!$$

Commented by cortano1 last updated on 02/Oct/22

$$\mathrm{nice}$$

Commented by Tawa11 last updated on 02/Oct/22

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

Answered by mr W last updated on 01/Oct/22

Commented by mr W last updated on 01/Oct/22

$$BC=4+8+9=21$$$$AB=4+6+a=21\Rightarrow a=11$$$$AC=a+b+9=21\Rightarrow b=1$$$$perimeter=6+4+8+9+a+b=39✓$$

Commented by cortano1 last updated on 01/Oct/22

$$\frac{\mathrm{a}}{21}=\frac{\mathrm{a}}{\mathrm{a}+\mathrm{b}+9}\Rightarrow \mathrm{a}+\mathrm{b}+9=21$$$$\frac{9}{10+\mathrm{a}}=\frac{9}{9+\mathrm{a}+\mathrm{b}}\Rightarrow 10+\mathrm{a}=9+\mathrm{a}+\mathrm{b}$$$$\Rightarrow \mathrm{b}=1\mathrm{\&}\mathrm{a}=11$$$$\mathrm{perimeter}=6+8+4+11+1+9=39$$$${\mathrm{it}}^{\prime }\mathrm{correct}?$$

Commented by mr W last updated on 01/Oct/22

$$ok.$$$$butyouhavedirectly21=a+b+9,$$$$noneedfrom\frac{\mathrm{a}}{21}=\frac{\mathrm{a}}{\mathrm{a}+\mathrm{b}+9}.$$$$since\mathrm{\Delta }ABCisequilateral.$$

Answered by a.lgnaoui last updated on 01/Oct/22

$$\mathrm{P}osonsy=\mathrm{CD}x=\mathrm{DE}$$$$y=\mathrm{CD}={\mathrm{HH}}^{\prime }=\mathrm{HF}+{\mathrm{FH}}^{{}^{\prime }}$$$$dapreslafigure\measuredangle \mathrm{ABO}=\measuredangle \mathrm{BAO}=60donc\mathrm{OB}=\mathrm{OA}=\mathrm{AB}=4\Rightarrow \mathrm{OC}=10$$$$\sin 60=\frac{\mathrm{CH}}{10}=\frac{\sqrt{3}}{2}\Rightarrow \mathrm{CH}=5\sqrt{3}$$$$\cos 60=\frac{1}{2}=\frac{4+\mathrm{AH}}{10}\Rightarrow \mathrm{AH}=1\mathrm{A}\Rightarrow \mathrm{HF}=7$$$$calculde{\mathrm{FH}}^{{}^{\prime }}$$$${\mathrm{FEO}}^{{}^{\prime }}={\mathrm{EO}}^{{}^{\prime }}\mathrm{F}=60\Rightarrow \mathrm{EF}={\mathrm{EO}}^{{}^{\prime }}=9$$$$\mathrm{OD}=x+9\Rightarrow \sin 60=\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{9+x}\Rightarrow x=1$$$$donc\mathrm{DE}=1$$$${\mathrm{FD}}^2=9^2+{\mathrm{x}}^2-18\cos 120=82+9=91\Rightarrow \mathrm{FD}=\sqrt{91}$$$$\mathrm{FD}=\sqrt{{\mathrm{FD}}^2-{\mathrm{FF}}^{\prime 2}}=\sqrt{91-75}=4\Rightarrow {\mathrm{F}}^{\prime }\mathrm{D}=4$$$$alors$$$$\mathrm{D}onc\mathrm{CD}=7+4=11$$$$finalement$$$$Peeimetre=4+6+8+9+1+11=39$$$$$$

Commented by a.lgnaoui last updated on 01/Oct/22

Commented by a.lgnaoui last updated on 01/Oct/22

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