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PS - Area of shaded region [#permalink]
 14 Oct 2005, 22:04
Question Stats:
0% (00:00) correct
 0% (00:00) wrong based on 0 sessions
See Attached... took me > 3mins to solve ... shorter method?
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PS - Area.gif [ 2.68 KiB | Viewed 394 times ]
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-Vikram
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BD= sqrt ( 20^2+15^2) = 25
BD* CE = 20*15=300 ---->CE = 12
BE= sqrt ( 20^2-12^2) = 16
The area is : 12*16/2= 96
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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
Area = 1/2*16*12 = 96
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Another method: (It took me little less than 2 mins)
1) Find the area of the triangle BCD = 1/2 * b * h = 1/2 * 20 * 15 = 150
2) Find the area of the triangle CED.
hypotenuse is 15 (Remember the ratio is 3:4:5 - hence the sides should be 9:12:15)
area = 1/2 * 12 * 9 = 54
3) Area of shaded region = area BCD - area CED = 150 - 54 = 96
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thanks guys... Keep forgetting about similar triangles!!
And yes, OA is 96.
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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...
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I dont think you can assume its 3:4:5 triangle'
what if its is 5:12:13?
sudhagar wrote: Another method: (It took me little less than 2 mins)
1) Find the area of the triangle BCD = 1/2 * b * h = 1/2 * 20 * 15 = 150
2) Find the area of the triangle CED.
hypotenuse is 15 (Remember the ratio is 3:4:5 - hence the sides should be 9:12:15)
area = 1/2 * 12 * 9 = 54
3) Area of shaded region = area BCD - area CED = 150 - 54 = 96
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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 
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Current Student
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First of it should be 6 triangles...
so lets see..
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 |
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Re: PS - Area of shaded region [#permalink]
15 Oct 2005, 10:41
vikramm wrote: See Attached... took me > 3mins to solve ... shorter method?
took me 30 seconds
notice the 9:12:15 triangle
know your squares
15^2 and 20^2 = 625
hype is 25
base is 25 - 9 = 16
16*12 = 192/2 = 96
knowing your 3:4:5s, 5:12:13s, and 8:15:17s saves a heck of a lot time!  (geek)
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bigtooth81 wrote: I got C
Bigtooth your avatar is quite sultry.
I think you should replace it with this one which I think is more politically correct: 
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or this 
(better match  )
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gsr wrote: or this (better match ) No. Yours is way too raunchy GSR. Your emoticons are French kissing.
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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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HongHu wrote: 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.
I also agree that this is the best approach ^_^
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