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PS: Triangle

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PS: Triangle [#permalink]

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New post 13 Feb 2009, 03:51
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Senior Manager
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Re: PS: Triangle [#permalink]

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New post 13 Feb 2009, 04:27
We have 3 right angle triangles psq,qsr and pqr.

for PSQ PQ^2-256 = QS^2 -- 1
for QSR RQ^2 - 81 = QS^2 -- 2
then solve both you will find PQ2 - RQ^2 = 175 -- 3
from PQR PQ^2 + QR^2 = 625 --- 4

Solve eqn 3 qnd 4 PQ^2 = 400 . Sub in 1 and find QS^2 = 144 so QS = 12

so area of triangle PQR = 1/2* 25* 12 = 150.

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Re: PS: Triangle [#permalink]

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New post 13 Feb 2009, 08:38
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There is one formula that is worth remembering.

In a right triangle, when a perpendicular(altitude) is drawn from the vertex opposite to hypotenuse on the hypotenuse, then

(length of the altitude)^2 = product of the segments that it divides on the hypotenuse.

Based on the given figure, applying the above formula,
\((QS)^2 = PS * SR\) ==> \(QS = sqrt(16 * 9) = 12.\)

Now height is known, base is known. Applying the formula we get area of the trainagle to be 150.

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Re: PS: Triangle [#permalink]

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New post 13 Feb 2009, 14:27
mrsmarthi wrote:
There is one formula that is worth remembering.

In a right triangle, when a perpendicular(altitude) is drawn from the vertex opposite to hypotenuse on the hypotenuse, then

(length of the altitude)^2 = product of the segments that it divides on the hypotenuse.

Based on the given figure, applying the above formula,
\((QS)^2 = PS * SR\) ==> \(QS = sqrt(16 * 9) = 12.\)

Now height is known, base is known. Applying the formula we get area of the trainagle to be 150.


great!!!
How did you derive that?

+1 for you.
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Re: PS: Triangle [#permalink]

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New post 13 Feb 2009, 17:48
excellent formula.Thank you very much

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Re: PS: Triangle [#permalink]

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New post 13 Feb 2009, 18:05
x2suresh wrote:
mrsmarthi wrote:
There is one formula that is worth remembering.

In a right triangle, when a perpendicular(altitude) is drawn from the vertex opposite to hypotenuse on the hypotenuse, then

(length of the altitude)^2 = product of the segments that it divides on the hypotenuse.

Based on the given figure, applying the above formula,
\((QS)^2 = PS * SR\) ==> \(QS = sqrt(16 * 9) = 12.\)

Now height is known, base is known. Applying the formula we get area of the trainagle to be 150.


great!!!
How did you derive that?

+1 for you.


I got this formula from one of the forums / net and made it's entry into my flashcard list. :)

But if you are interested in the derivation, here is the link

http://www.cliffsnotes.com/WileyCDA/Cli ... 18818.html

Enjoy.........

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Re: PS: Triangle [#permalink]

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New post 14 Feb 2009, 09:45
mrsmarthi wrote:
x2suresh wrote:
mrsmarthi wrote:
There is one formula that is worth remembering.

In a right triangle, when a perpendicular(altitude) is drawn from the vertex opposite to hypotenuse on the hypotenuse, then

(length of the altitude)^2 = product of the segments that it divides on the hypotenuse.

Based on the given figure, applying the above formula,
\((QS)^2 = PS * SR\) ==> \(QS = sqrt(16 * 9) = 12.\)

Now height is known, base is known. Applying the formula we get area of the trainagle to be 150.


great!!!
How did you derive that?

+1 for you.


I got this formula from one of the forums / net and made it's entry into my flashcard list. :)

But if you are interested in the derivation, here is the link

http://www.cliffsnotes.com/WileyCDA/Cli ... 18818.html

Enjoy.........



Thats real cool. 8-)

+1 for the formula.
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Re: PS: Triangle [#permalink]

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New post 14 Feb 2009, 09:54
wow...really neat +1

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Re: PS: Triangle [#permalink]

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New post 15 Feb 2009, 10:52
The other easy and quick way to do this problem is to recognize that the problem states the large triangle is a right triangle and it gives you the length of its hypotenuse which is 25 (the addition of the two segments....16+9). One of the rules of a right triangle is that if the hypotenuse is 5, then the other two sides have lengths of 3 and 4. (Perhaps you have heard of a 3:4:5 triangle?). Since 25 is a multiple of 5, you can recognize that this is a multiple of a 3:4:5 triangle. So the other two sides (the base and height) are 15 and 20.

A = (1/2)b*h
A = (1/2)*20*15
A = 10*15
A = 150

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Re: PS: Triangle   [#permalink] 15 Feb 2009, 10:52
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