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Question Number 95999 by i jagooll last updated on 29/May/20

Answered by mr W last updated on 29/May/20

Commented by mr W last updated on 29/May/20

BE=BA+ED is clear.  error in calculating x is fixed.

$${BE}={BA}+{ED}\:{is}\:{clear}. \\ $$$${error}\:{in}\:{calculating}\:{x}\:{is}\:{fixed}. \\ $$

Commented by john santu last updated on 29/May/20

check..sir. it wrong

$$\mathrm{check}..\mathrm{sir}.\:\mathrm{it}\:\mathrm{wrong}\: \\ $$

Commented by mr W last updated on 29/May/20

BE=BF+FD=BA+ED=6+6−x  (√(6^2 +x^2 ))=12−x  6^2 =12^2 −24x  ⇒x=((12^2 −6^2 )/(24))=(9/2)  A_(shadeed) =(6/2)×(9/2)=((27)/2)

$${BE}={BF}+{FD}={BA}+{ED}=\mathrm{6}+\mathrm{6}−{x} \\ $$$$\sqrt{\mathrm{6}^{\mathrm{2}} +{x}^{\mathrm{2}} }=\mathrm{12}−{x} \\ $$$$\mathrm{6}^{\mathrm{2}} =\mathrm{12}^{\mathrm{2}} −\mathrm{24}{x} \\ $$$$\Rightarrow{x}=\frac{\mathrm{12}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} }{\mathrm{24}}=\frac{\mathrm{9}}{\mathrm{2}} \\ $$$${A}_{{shadeed}} =\frac{\mathrm{6}}{\mathrm{2}}×\frac{\mathrm{9}}{\mathrm{2}}=\frac{\mathrm{27}}{\mathrm{2}} \\ $$

Commented by bobhans last updated on 29/May/20

what formula BE = BA + ED?

$$\mathrm{what}\:\mathrm{formula}\:\mathrm{BE}\:=\:\mathrm{BA}\:+\:\mathrm{ED}? \\ $$

Commented by john santu last updated on 29/May/20

oo yes. great

$$\mathrm{oo}\:\mathrm{yes}.\:\mathrm{great} \\ $$

Answered by john santu last updated on 29/May/20

Commented by john santu last updated on 29/May/20

BF^2 =BC^2 +CF^2   (6+x)^2 = 6^2 +(6−x)^2   (6+x)^2 −(6−x)^2 =36  (12)(2x)=36 ⇒x = (3/2)  CF = 6−(3/2) = (9/2)  shaded area = ((6×(9/2))/2)= ((27)/2)  is the answer

$$\mathrm{BF}^{\mathrm{2}} =\mathrm{BC}^{\mathrm{2}} +\mathrm{CF}^{\mathrm{2}} \\ $$$$\left(\mathrm{6}+\mathrm{x}\right)^{\mathrm{2}} =\:\mathrm{6}^{\mathrm{2}} +\left(\mathrm{6}−\mathrm{x}\right)^{\mathrm{2}} \\ $$$$\left(\mathrm{6}+\mathrm{x}\right)^{\mathrm{2}} −\left(\mathrm{6}−\mathrm{x}\right)^{\mathrm{2}} =\mathrm{36} \\ $$$$\left(\mathrm{12}\right)\left(\mathrm{2x}\right)=\mathrm{36}\:\Rightarrow\mathrm{x}\:=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{CF}\:=\:\mathrm{6}−\frac{\mathrm{3}}{\mathrm{2}}\:=\:\frac{\mathrm{9}}{\mathrm{2}} \\ $$$$\mathrm{shaded}\:\mathrm{area}\:=\:\frac{\mathrm{6}×\frac{\mathrm{9}}{\mathrm{2}}}{\mathrm{2}}=\:\frac{\mathrm{27}}{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{answer}\: \\ $$

Commented by bobhans last updated on 29/May/20

good

$$\mathrm{good}\: \\ $$

Commented by i jagooll last updated on 29/May/20

yes sir it correct

$$\mathrm{yes}\:\mathrm{sir}\:\mathrm{it}\:\mathrm{correct} \\ $$

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