Respuesta :
Answer:
Circumference of circle A = 81.38 feet
Area of circle A = 530.66 square feet
Step-by-step explanation:
We are given the following in the question:
Let r be the radius of circle A.
Then, diameter of circle A = 2r
Let s be diameter of circle B.
The radius of Circle A is three feet less than twice the diameter of Circle B.
Thus, we can write the equation:
[tex]r = 2s-3\\\Rightarrow 2s-r = 3[/tex]
The sum of the diameters of both circles is 49 feet.
Thus, we can write the equation:
[tex]2r + s = 49[/tex]
Solving the two equations, we get,
[tex]2r + s + 2r-s = 49 + 3\\4r = 52\\\Rightarrow r = 13[/tex]
Thus, radius of circle A is 13 feet.
Circumference of circle A =
[tex]C = 2\pi r\\C =2\times 3.13\times 13 \\C = 81.38\text{ feet}[/tex]
Area of circle A =
[tex]A = \pi r^2\\A =3.14\times (13)^2\\A = 530.66\text{ square feet}[/tex]
