Question

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

Answer 1

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.

Answer 2

What does that mean?

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

^^ what they said

Answer 7

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

Answer 8

got it okay thanks phi!!!! <333