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# Math: Triangles

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Intern
Joined: 14 May 2010
Posts: 5

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17 Jun 2010, 12:06
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
Math Expert
Joined: 02 Sep 2009
Posts: 39702

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18 Jun 2010, 02:14
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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Intern
Joined: 14 May 2010
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21 Jun 2010, 10:25
Thank you for the explanation
Manager
Joined: 23 Oct 2009
Posts: 84
Location: New Delhi, India
Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia

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06 Jul 2010, 06:00
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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Joined: 15 Mar 2010
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07 Jul 2010, 20:49
simply waoww.. wish i could have given you more than one +1...kudos
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Manager
Joined: 04 Feb 2010
Posts: 195

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07 Jul 2010, 23:33
Wow, thanks for this summary!
Intern
Joined: 11 Jul 2010
Posts: 2

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22 Jul 2010, 03:25
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.'

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!
Math Expert
Joined: 02 Sep 2009
Posts: 39702

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22 Jul 2010, 04:06
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.'

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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Joined: 28 May 2010
Posts: 33

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24 Jul 2010, 07:01
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?
Math Expert
Joined: 02 Sep 2009
Posts: 39702

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24 Jul 2010, 08:30
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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Joined: 16 Feb 2010
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30 Aug 2010, 14:22
amazing! one day GMATclub might get to publish its own book : )
Intern
Joined: 03 Aug 2010
Posts: 22

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31 Aug 2010, 23:03
This is awesome...thanks!!!!
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Welcome to my paintings website - Wholesale Art Mall.

Intern
Joined: 01 Oct 2010
Posts: 4

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10 Oct 2010, 23:14
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.
Intern
Joined: 10 Aug 2007
Posts: 4

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16 Oct 2010, 09:48
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
Manager
Joined: 01 Nov 2010
Posts: 177
Location: Zürich, Switzerland

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10 Nov 2010, 14:36
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.
Intern
Joined: 01 Jan 2011
Posts: 1

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06 Jan 2011, 11:55
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 ...
Manager
Joined: 02 Oct 2010
Posts: 149

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11 Jan 2011, 12:18
Excellent post.
I went through all this triangle formulas and it is very very helpful......
Intern
Joined: 11 May 2008
Posts: 8

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04 Feb 2011, 14:13
A very useful collection !! Thank you! - +
Manager
Joined: 18 Aug 2010
Posts: 90

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05 Feb 2011, 14:29
Material is Great !!!
+ KUDO FROM ME
Senior Manager
Joined: 19 Oct 2010
Posts: 261
Location: India
GMAT 1: 560 Q36 V31
GPA: 3

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22 Apr 2011, 07:11
Hi Bunuel,

Can you please explain the last point in the median section?
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Re: Math: Triangles   [#permalink] 22 Apr 2011, 07:11

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