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96
laxieqv is probably quicker, this was how I did it

DB = sqrt(400+225) = 25
Area (BCD) = 05*20*15 = 05*25*CE => CE = 12
Tri BEC ~ Tri CED (note order of vertices)
=> BE/CE = BC/CD =20/15
=> BE = 20*12/15 = 16

well I figured (1) the entire area has to be less than half of that of rectangle...i.e 150

then I said, how many right angle triangles can I cut in a rectangle...looks like 5, so I divide 300/5=60, so thats the area of each right angle triangle
then the area of the shaded area has to be 150-50=90 or very close to it...96 it is...took less than 40 seconds to do this...

well I figured (1) the entire area has to be less than half of that of rectangle...i.e 150

then I said, how many right angle triangles can I cut in a rectangle...looks like 5, so I divide 300/5=60, so thats the area of each right angle triangle then the area of the shaded area has to be 150-50=90 or very close to it...96 it is...took less than 40 seconds to do this...

Can you demonstrate how? I mean the bold part ....thank you ...just want to know how this very interesting solution works

if you look at the trinagle with one side equal to 15 (i.e. the prependicular) then you roughly sketch it on a piece of paper and you will see there are 6 such trinagles that you can cut...

each triangle would have an area roughly=50

so then you get 150 (from half the area of the rectangle)-50 its about 100.

laxieqv wrote:

fresinha12 wrote:

wow...i just estimated it to 96...

well I figured (1) the entire area has to be less than half of that of rectangle...i.e 150

then I said, how many right angle triangles can I cut in a rectangle...looks like 5, so I divide 300/5=60, so thats the area of each right angle triangle then the area of the shaded area has to be 150-50=90 or very close to it...96 it is...took less than 40 seconds to do this...

Can you demonstrate how? I mean the bold part ....thank you ...just want to know how this very interesting solution works

In my opinion knowing the 3:4:5 triangle is the best approach. The first step you notice that the big triangle is 5*(3:4:5), the second step you know the small triangle is also a 3:4:5 with the long side =15. You can figure out h=12 in like 30 seconds. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

In my opinion knowing the 3:4:5 triangle is the best approach. The first step you notice that the big triangle is 5*(3:4:5), the second step you know the small triangle is also a 3:4:5 with the long side =15. You can figure out h=12 in like 30 seconds.

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