## anonymous one year ago The area of a circle is equal to the area of a square. Which one is greater? A. circumference of the circle B. perimeter of the square

1. phi

you can figure it out, but it is "well-known" (to those who know it well) that the shortest perimeter enclosing a fixed area is that of a circle.

2. anonymous

What does that mean?

3. anonymous

it means the circle will always have the smallest perimeter compared to another shape

4. anonymous

so i don't have to go through steps to figure this out? The circle always has the smallest circumference/perimeter compared to every shape out there?

5. phi

if you did not know that, you start by saying $\pi r^2 = s^2 \\ s= r \sqrt{\pi}$ the perimeter of a circle vs square is $2 \pi r \ vs \ 4s \\2 \pi r \ vs\ 4r \sqrt{\pi}$ divide both sides by 2r sqr(pi) $\sqrt{\pi} \ vs\ 2$ pi is about 3.14 and its square root is less than the square root of 4 thus the perimeter of the circle is shorter

6. anonymous

^^ what they said

7. phi

** compared to every shape out there?*** yes, that have the same area

8. anonymous

got it okay thanks phi!!!! <333