# maximum area

• June 11th 2011, 08:13 AM
maximum area
show that triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.(using calculus only)
• June 12th 2011, 12:23 AM
FernandoRevilla

Math Forum - Ask Dr. Math
• June 12th 2011, 05:40 AM
Also sprach Zarathustra
Quote:

Originally Posted by FernandoRevilla

Math Forum - Ask Dr. Math

Can someone check this(?):

$S_{ABC}=\frac{abc}{4R}$ is the area of triangle inscribed in a given circle of radius R.

$max\{S_{ABC}\}=max\{\frac{abc}{4R}\}$

$max\{S_{ABC}\}=max\{\frac{a^3}{4R},\frac{b^3}{4R}, \frac{c^3}{4R}$ hence, [tex}a=b=c[/tex].
• June 12th 2011, 06:49 AM