All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
By all means (Posted on 2011-06-16) Difficulty: 3 of 5
In isosceles triangle AB=BC=n.

What value of AC warrants the largest area of the triangle ABC?
Solve by:
a) Plane geometry.
b) Trigonometry.
c) Calculus.
d) Any other way is welcome.

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
ths time by vectors Comment 5 of 5 |
The magnitude of the cross product of two 3-dimensional vectors is equal to the are of the parallelogram having the vectors as adjacent sides.  The triangle sought is half of this parallelogram.

The first vector, representing BA can be
v = ni + 0j + 0k
The second vector BC, forming an angle θ with u can be written as
w = ncos(θ) i + nsin(θ) j + 0k

The cross product vXw = 0i - 0j + nēsin(θ)
and so the magnitude ||vXw|| = nēsin(θ)

Which is maximized when θ=90š, so w becomes
w = 0i + nj + 0k

AC can be called vector z, which satisfies the relationship v+z=w or
z = w - v = -ni + nj + 0k

which has magnitude
||z|| = √((-n)ē+nē+0ē) = √(2nē) = n√2
  Posted by Jer on 2011-06-16 15:54:07
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information