Question

Can someone find r please

Answer 1

Answer:

$r = 3 \times \sqrt{2}$

Step-by-step explanation:

The area of the square is 36.

A = s^2

36 = s^2

s = sqrt(36)

s = 6

The side of the square has length 6.

All sides of a square are congruent, so all sides have length 6.

If you extend segment JO to point L, you end up with segment JL which is a diameter of the circle and the diagonal of the square. We can use the Pythagorean theorem using two sides if the square as legs and the diagonal of the square as the hypotenuse of a right triangle.

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

c^2 = 72

$c = \sqrt{72}$

$c = \sqrt{36 \times 2}$

$c = \sqrt{36} \times \sqrt{2}$

$c = 6 \times \sqrt{2}$

c is the diameter.

r is the radius, so it is half of the diameter.

c = d

r = d/2

$r = \dfrac{d}{2} = 3 \times \sqrt{2}$