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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

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).
_________________

My Practice GMAT Scores 29th Jan '11 -- GMATPrep#2 : 700 (Q47 V38) 23rd Jan '11 -- MGMAT Practice Test #3 : 670 (Q45 V36) 19th Jan '11 -- GMATPrep#1 v.1 : 710 (Q49 V37) 15th Jan '11 -- GMATPrep#1 : 720 (Q47 V42) 11th Jan '11 -- MGMAT Practice Test #2 : 740 (Q47 V44) 6th Jan '11 -- Kaplan#2 : 620 (Q40 V35) 28th Dec '10 -- PowerPrep#1 : 670 (Q47 V35) 30th Oct '10 -- MGMAT Practice Test #1 : 660 (Q45 V35) 12th Sept '10 -- Kaplan Free Test : 610 (Q39 V37) 6th Dec '09 -- PR CAT #1 : 650 (Q44 V37) 25th Oct '09 -- GMATPrep#1 : 620 (Q44 V34)

If you feel like you're under control, you're just not going fast enough. A goal without a plan is just a wish. You can go higher, you can go deeper, there are no boundaries above or beneath you.

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.

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.
_________________

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.

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 \(a\).
_________________

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.

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

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

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