The largest possible square that will fit into a circle 31 cm diameter is?

Question

The largest possible square that will fit into a circle 31 cm diameter is?

Answer 1

i will give you a hint:

When you have the square inside the circle, the diameter of the circle is the same as the diagonal of the square.

If you can relate the side length of the square to the diagonal length, you will have your answer!

good luck

Answer 2

Think of a square as two right angled, isosceles triangles adjoining each other.  The length of the diagonal, by Pythagoras' theorem, is the swuare root of (2*a^2) where a is thelength of a side of the square.  The largest square that can fit in the circle would have a diagonal equal in length to the diameter of the circle.  So just equate the root of (2*a^2) with 31 cm, and solve.

Answer 3

((31^2) / 2)^.5 = 21.9203102

edit:  interesting, thumb down.  wonder why.

what's the diagonal of a 21.92 " square?

((21.92^2) + (21.92^2))^.5 = 30.9995613

looks pretty close to me.