Find central angle and radius of word problem (see description.)

Question

A flower bed is planned in the form of a circular sector. Find the central angle and radius if it is to cover 625 feet, and its perimeter is to be a minimum. Write the exact answer. Do not round.

I need help with this, I could not find any examples and no one that I know understands it or remembers it. Please help!

Answer 1

This is messy but it works out easily!

Let x=the central angle in degrees, r the radius and P the perimeter.

(x/180)*πr² = 625 => x=625*180/(πr²)

P= 2r+(x/180)*2πr => P=2r + [625*180*2πr/(180πr²) => P =2r + (1250/r)

dP/dr= 2 - (1250/r²) = 0 at the minimum

r² = 625

You finish i from here!!!!