Please help and explain process if possible.

Question

A rug company sells circular rugs that have a uniform circular border. The area of the border is about half the area of the circular rug it surrounds. If the radius of the entire rug is 10.0 m, what is the width of the border?

Answer 1

slightly less than 2 1/4 meters = width of the border

Area of the rug = 100pi

Area of the border = 50pi

Area of both = 150pi = pi(r)^2 where r = radius of the enclosed area, rug+border

150pi = pi(r)^2 the pi's cancel leaving

150 = r^2

r = sqr150 = about 12.25

12.25-10 = 2.25 meters = width of the border