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Question Number 69608 by TawaTawa last updated on 25/Sep/19

Commented by Prithwish sen last updated on 27/Sep/19

a) ∣AB∣=2(√2)= 2.8m  b) perimeter of ALB =((2×π×2×270)/(360))m= 9.4m

$$\left.\boldsymbol{\mathrm{a}}\right)\:\mid\boldsymbol{\mathrm{AB}}\mid=\mathrm{2}\sqrt{\mathrm{2}}=\:\mathrm{2}.\mathrm{8m} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{perimeter}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{ALB}}\:=\frac{\mathrm{2}×\pi×\mathrm{2}×\mathrm{270}}{\mathrm{360}}\mathrm{m}=\:\mathrm{9}.\mathrm{4m} \\ $$

Commented by TawaTawa last updated on 25/Sep/19

God bless you sir, please show more steps

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir},\:\mathrm{please}\:\mathrm{show}\:\mathrm{more}\:\mathrm{steps} \\ $$

Answered by mind is power last updated on 25/Sep/19

AB=2AM  AM=OAcos(OAM)  OAM=(π/4)  ⇒AM=R.cos(45)=2.((√2)/2)=(√2)  b)AL=LB  AL^2 =AM^2 +ML^2 =AM^2 +(OM+ML)^2 =2+((√2)+2)^2 =10+4(√2)  AL=(√(10+4(√2)))  perimeter=2.AL+2AM=2(√(10+4(√2)))+2(√2)

$${AB}=\mathrm{2}{AM} \\ $$$${AM}={OAcos}\left({OAM}\right) \\ $$$${OAM}=\frac{\pi}{\mathrm{4}} \\ $$$$\Rightarrow{AM}={R}.{cos}\left(\mathrm{45}\right)=\mathrm{2}.\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}=\sqrt{\mathrm{2}} \\ $$$$\left.{b}\right){AL}={LB} \\ $$$${AL}^{\mathrm{2}} ={AM}^{\mathrm{2}} +{ML}^{\mathrm{2}} ={AM}^{\mathrm{2}} +\left({OM}+{ML}\right)^{\mathrm{2}} =\mathrm{2}+\left(\sqrt{\mathrm{2}}+\mathrm{2}\right)^{\mathrm{2}} =\mathrm{10}+\mathrm{4}\sqrt{\mathrm{2}} \\ $$$${AL}=\sqrt{\mathrm{10}+\mathrm{4}\sqrt{\mathrm{2}}} \\ $$$${perimeter}=\mathrm{2}.{AL}+\mathrm{2}{AM}=\mathrm{2}\sqrt{\mathrm{10}+\mathrm{4}\sqrt{\mathrm{2}}}+\mathrm{2}\sqrt{\mathrm{2}} \\ $$

Commented by TawaTawa last updated on 25/Sep/19

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by mind is power last updated on 26/Sep/19

y′re welcom

$${y}'{re}\:{welcom} \\ $$

Commented by TawaTawa last updated on 26/Sep/19

Sir, please help me check. the perimeter here is  9.4  but your annswer  is  10.7

$$\mathrm{Sir},\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{check}.\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{here}\:\mathrm{is}\:\:\mathrm{9}.\mathrm{4}\:\:\mathrm{but}\:\mathrm{your}\:\mathrm{annswer} \\ $$$$\mathrm{is}\:\:\mathrm{10}.\mathrm{7} \\ $$

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