A simple question

[dttom]

http://www2.hkedcity.net/sch_files/a/kst/kst-07110/photo_album/200511/204962/507977820.JPG

Addition: AD=e

Anyone can help me with the above question please?

 

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[woelen]

The problem is not clear to me. Which parameter is varied, what is kept constant?

[dttom]

e,a, and b is variables;

a+b=45 degree

0<=(a)<=45

[cosine]

e' date='a, and b is variables;

a+b=45 degree

0<=(a)<=45[/quote']

 

Where is e?

[dttom]

Where is e?

Addition: AD=e

 

AD=e

[uncool]

You want the greatest possible value of AB*AC for this, because Area = AB*AC * sin(A)/2

AB = e cos(a)

AC = e cos(45-a)

AB*AC = e^2*cos(a)cos(45-a)

AB*AC*sin(A)/2 = e^2*cos(a)cos(45-a)sqrt(2)/4

The maximum is when a = 45 - a, or a = 22.5.

e^2*cos(22.5)^2*sqrt(2)/4 = e^2*(cos(45)+1)*sqrt(2)/8

= e^2*(1 + sqrt(2))/8

=Uncool=