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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    
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A trigonometry way | Comment 1 of 5
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 0 to 180

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=90 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)

n+ n= (AC)

AC = n√2

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