An isosceles triangle inscribed in a circle. How should this be accomplished if triangle’s area is maximized?!?
An isosceles triangle is placed inside a circle of radius r with its vetices on the boundary of the circle. How should this be accomplished if the area of the triangle is to be maximized?
This problem relates to using derivatives… I have no idea what to do or how to set it up.. can someone please help? Thank you so much!
Draw a triangle in a circle with a height greater than the radius. The height is r+x.
The 1/2 of the base is sqrt(r^2 – x^2).
The area is A = (1/2) b h = (r+x)*sqrt(r^2 – x^2)
The max area occurs when dA/dx =0
Compute the derivative and solve for the value of x as a fraction of r or simply let r=1.
Draw a triangle in a circle with a height greater than the radius. The height is r+x.
The 1/2 of the base is sqrt(r^2 – x^2).
The area is A = (1/2) b h = (r+x)*sqrt(r^2 – x^2)
The max area occurs when dA/dx =0
Compute the derivative and solve for the value of x as a fraction of r or simply let r=1.
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