Question

Just want some hints as I want to figure this out - suppose you inscribe a triangle inside a circle of radius 2cm use calculus to find largest area possible for this triangle :)

Answer 1

@hartnn

Answer 2

@iambatman

Answer 3

@Jemurray3

Answer 4

Things I have been pushing in my head equation of circle is x^2+y^2=4
Also 1/2bh for area of triangle

Answer 5

inscribe triangle all angles are the same (60) so sides length

Answer 6

So if all same a for sides equilateral triangle so area =root3/4*s^2 ?

Answer 7

herons theorem
s=(a+a+a)/2=3/2a

Answer 8

area=sqr(3/2a*(3/2a-a)^3)
area=sqr(3/2a*(3/2a-2/2a)^3)...........add 2/2 in second term
=sqr(3/2a*(a/2)^3)=a^2/4sqr(3)

Answer 9

area=(a^2 sqr(3))/4=((2sqr(3))^2*sqr(3))/4=4*3*sqr(3)/4=3*sqr(3)

Answer 10

\[area=3\sqrt{3}\]