BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

altitude of a equilateral

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Quantitative Reasoning |
Master | Next Rank: 500 Posts
Posts: 161
Joined: Mon Apr 05, 2010 9:06 am
Location: Mumbai
Thanked: 37 times

by 4GMAT_Mumbai » Sun Aug 15, 2010 9:06 am
Let ABC be the triangle.

Let AD be the median from A to BC. In an equilateral triangle, median is same as the height.

So, Angle of ADC = 90 degrees.

So, ADC is a right angled triangle with AC as the hypotenuse.

If 'a' is the length of a side,

AC = a units
DC = (a/2) units. (as AD is the median to BC).

Using Pythagorus theorem, one can deduce that AD = height of the equi triangle = side * sqrt(3)/2

Hope this helps. Thanks.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
Top
User avatar
Legendary Member
Posts: 1255
Joined: Fri Nov 07, 2008 2:08 pm
Location: St. Louis
Thanked: 312 times
Followed by:90 members

by Tani » Sun Aug 15, 2010 4:19 pm
If you know the ratio of the sides of a 30-60-90 triangle you can quickly get to the altitude of an equilateral. Try drawing a 30-60-90. Your short leg will be x, the hypotenuse 2x and the other leg x times the square root of three. Then rotate that triangle around the longer leg (the x root3 leg). You will have a 60-60-60 triangle (equilateral). The sides will be 2x and the altitude x root 3.

Similarly, the 45-45-90 triangle when rotated around the hypotenuse gives you a square. So the diagonal of a square is always the side times the square root of 2.

Two great short cuts when dealing with mixed figures!
Tani Wolff
Top
Post new topic Post Reply
• Page 1 of 1