SOLUTION: A circle placed between outer square and inner square. the length of the outer square wall is 10. How to find formula of the circle radius and length of inner square wall?

Question 893879: A circle placed between outer square and inner square. the length of the outer square wall is 10. How to find formula of the circle radius and length of inner square wall?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the diameter of the circle will be equal to the length of the outer square wall.

the diameter of the circle will be equal to the length of a diagonal of the inner square.

the length of the outer square wall is equal to 10.

the diameter of the circle is also equal to 10.

the length of the inner square wall is equal to square root of 50.

this is because the diameter of the smaller square is a hypotenuse of the right triangle that has the side of the smaller square as its legs.

if we allow the length of the inner square wall be equal to x, by pythagorus, we get x^2 + x^2 = 10^2 which becomes 2x^2 = 100 which becomes x^3 = 50 which becomes square root of x = square root of 50.

this assumes the inner square is inscribed in the circle and the outer square has the circle inscribed into it.

the following diagram shows you what i believe is the problem you posted.

$$$

RELATED QUESTIONS
There are two circles, one circle is inscribed and another circle is circumscribed over a (answered by ajmisra)

Kidney outer and inner shape. If I know the distance in feet around the outer irregular... (answered by ikleyn,Alan3354)

the radius of the outer circle is 8 cm, the radius of the inner circle is 5 cm, and the... (answered by Alan3354)

A circle is inscribed in a square, which is inscribed in an equilateral triangle... (answered by greenestamps)

how do I find the area of a donut when I only have the radius of the outer circle?... (answered by dabanfield,richwmiller)

find the area of an annulus when inner circle diameter is 6 and outer circle is... (answered by Alan3354)

How do I solve this? Q. Given two concentric circles, find the length of the radius of... (answered by DrBeeee)

find the shaded area of the outer circle. The length of the radius of the outer circle is (answered by jojo14344)

the area of a square pond is 1000 square m. A path of uniform width is surrounded outside (answered by josgarithmetic)