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.

An area formula for a triangle is A=.5*a*b*sin(C) where C is the angle between the two known sides and can be anything from 0º to 180º

Since we have two sides of fixed length, n, the area is solely dependent on sin(C).  This has a maximum value of 1 when C=90º which means angle ABC is a right angle so AC can be found via the Pythagorean Theorem (or the law of cosines if you want to keep in the trig theme)

n²+ n²= (AC)²

AC = n√2

Posted by Jer on 2011-06-16 14:49:38