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Math: Triangles

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Re: Math: Triangles [#permalink] New post 18 Jun 2010, 01:14
Expert's post
bely202 wrote:
Quote:
Usually called "half of base times height", the area of a triangle is given by the formula below.
• A=\frac{hb}{2}

Other formula:
• A=\frac{P*r}{2}

• A=\frac{abc}{4R}

Where b is the length of the base, a and c the other sides; h is the length of the corresponding altitude; R is the Radius of circumscribed circle; r is the radius of inscribed circle; P is the perimeter


Just to clarify, is P the perimeter of the circle or the triangle?
Quote:
• For an isosceles triangle with given length of equal sides right triangle (included angle) has the largest area.


Will u elaborate on this please? I'm not sure how this works.

Thanks a lot of the summary, very complete and succinct! :D


1. P is the perimeter of the triangle.
2. For instance if we have an isosceles triangle with equal sides of 1, the area will be greatest when it is a right angled triangle (max area in this case would be 1/2).
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Math: Triangles [#permalink] New post 21 Jun 2010, 09:25
Thank you for the explanation :)
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Re: Math: Triangles [#permalink] New post 06 Jul 2010, 05:00
Under Insoceles triangle section:
To find the base given the leg and altitude, use the formula:...

How do you derive these formulae? What's the logic behind them???
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Re: Math: Triangles [#permalink] New post 07 Jul 2010, 19:49
simply waoww.. wish i could have given you more than one +1...kudos :clap:
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Re: Math: Triangles [#permalink] New post 07 Jul 2010, 22:33
Wow, thanks for this summary! :)
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Re: Math: Triangles [#permalink] New post 22 Jul 2010, 02:25
Under Equilateral triangles its been mentioned that "For any point P within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle.'

Could you please help me out with this? I am not able to comprehend.

Also are the perpendicular bisectors and the altitudes the same in case of an equilateral triangles.

Thanks Bunuel!!! I am hunting and tracking down every post that your have posted in this forum. All of them that I have read till now have been extremely clear, precise and are tuned to the GMAT.

Thanks again! :)
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Re: Math: Triangles [#permalink] New post 22 Jul 2010, 03:06
Expert's post
sanram2205 wrote:
Under Equilateral triangles its been mentioned that "For any point P within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle.'

Could you please help me out with this? I am not able to comprehend.

Also are the perpendicular bisectors and the altitudes the same in case of an equilateral triangles.

Thanks Bunuel!!! I am hunting and tracking down every post that your have posted in this forum. All of them that I have read till now have been extremely clear, precise and are tuned to the GMAT.

Thanks again! :)


You won't need first one for GMAT.

As for the second question: in equilateral triangle angle bisectors, medians and altitudes (heights) are the same and equal in length.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Math: Triangles [#permalink] New post 24 Jul 2010, 06:01
Quote:
m=\sqrt{\frac{2b^2+2c^2-a^2}{4}}, where a, b and c are the sides of the triangle and a is the side of the triangle whose midpoint is the extreme point of median m.


What does extreme point of median m mean?
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Re: Math: Triangles [#permalink] New post 24 Jul 2010, 07:30
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knabi wrote:
Quote:
m=\sqrt{\frac{2b^2+2c^2-a^2}{4}}, where a, b and c are the sides of the triangle and a is the side of the triangle whose midpoint is the extreme point of median m.


What does extreme point of median m mean?


Extreme point is end point. All above means that median m is drawn to side a.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Math: Triangles [#permalink] New post 30 Aug 2010, 13:22
amazing! one day GMATclub might get to publish its own book : )
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Re: Math: Triangles [#permalink] New post 31 Aug 2010, 22:03
This is awesome...thanks!!!!
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Re: Math: Triangles [#permalink] New post 10 Oct 2010, 22:14
gmatdelhi wrote:
Under Insoceles triangle section:
To find the base given the leg and altitude, use the formula:...

How do you derive these formulae? What's the logic behind them???


The explanation is based on simple fact that -
In an Isosceles triangle the Altitude (coming from the vertex holding equal sides to the base) is Same as its Median.
ie., Altitude ( which forms 90 degrees with base cuts the base in 2 equal parts)..
Therefore Applying Phythogras theorem for

L is hypotenuse
A is side
B/2 is another side

Therefore L square = A Square + (B/2) Square

All the 3 formulas shown in the page are same , and derived from this only.

Hope this clarifies.

Regards,
Sridhar.
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Re: Math: Triangles [#permalink] New post 16 Oct 2010, 08:48
Another useful property for triangles,

If the sum of any two angles of a triangle equals the third angle then the triangle must be a right triangle
i.e. If the angles of a triangle are A, B and C, Then

=> A + B = C

But for any triangle A + B + C = 180

=> 2C = 180 or C = 90
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Re: Math: Triangles [#permalink] New post 10 Nov 2010, 13:36
Quote:
In similar triangles, the sides of the triangles are in some proportion to one another.



Hey Bunuel, a very small correction.

Above statement should be - In similar triangles, the sides of the triangles are in same proportion to one another.
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Re: Math: Triangles [#permalink] New post 06 Jan 2011, 10:55
Wow thank you so much!! This will be the great GMAT math book since sliced bread

Medians woah!!!! What I would do in a GMAt exam if I knew all these facts, I would beat the GMAT!

Writing in two day sand this is my final brush up of all my concepts ... great job ...
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Re: Math: Triangles [#permalink] New post 11 Jan 2011, 11:18
Excellent post.
I went through all this triangle formulas and it is very very helpful......
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Re: Math: Triangles [#permalink] New post 04 Feb 2011, 13:13
A very useful collection !! Thank you! - +
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Re: Math: Triangles [#permalink] New post 05 Feb 2011, 13:29
Material is Great !!!
+ KUDO FROM ME
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Re: Math: Triangles [#permalink] New post 22 Apr 2011, 06:11
Hi Bunuel,

Can you please explain the last point in the median section?
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Re: Math: Triangles [#permalink] New post 22 Jul 2011, 21:59
Thanks Bunuel :-D ... kudos...
Re: Math: Triangles   [#permalink] 22 Jul 2011, 21:59
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