Answer:
Area of Circle A = 1133.54
Circumference of Circle A= 119.32
Step-by-step explanation:
Given: Sum of both circle diameters= 49 feet.
Circle A radius= Three feet less than twice the diameter of circle B.
Lets assume diameter of Circle B is "x"
∴ Circle A radius (r)= ![(2x-3)](https://tex.z-dn.net/?f=%282x-3%29)
We know, the diameter of circle is ![2r](https://tex.z-dn.net/?f=2r)
Diameter of Circle A is ![2\times (2x-3)](https://tex.z-dn.net/?f=2%5Ctimes%20%282x-3%29)
Next as given sum of both circle diameter is 49 feet.
∴ ![2(2x-3)+x= 49\ feet](https://tex.z-dn.net/?f=2%282x-3%29%2Bx%3D%2049%5C%20feet)
distributing 2 with 2x and -3
⇒ ![4x-6+x= 49](https://tex.z-dn.net/?f=4x-6%2Bx%3D%2049)
⇒![5x-6= 49](https://tex.z-dn.net/?f=5x-6%3D%2049)
Adding both side by 6
⇒![5x=55](https://tex.z-dn.net/?f=5x%3D55)
Cross multiplying both side.
⇒![x=\frac{55}{5} = 11](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B55%7D%7B5%7D%20%3D%2011)
∴ Diameter of circle B is 11 feet.
Next, subtituting the value of x to get the value of radius for Circle A.
Radius of circle A= ![(2x-3)](https://tex.z-dn.net/?f=%282x-3%29)
⇒ Radius of circle A= ![(2\times 11-3)= 22-3](https://tex.z-dn.net/?f=%282%5Ctimes%2011-3%29%3D%2022-3)
∴ Radius of circle A= 19 feet.
Area of circle= ![\pi r^{2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D)
Taking π= 3.14
Area of circle A= ![3.14\times 19^{2} = 3.14\times 361](https://tex.z-dn.net/?f=3.14%5Ctimes%2019%5E%7B2%7D%20%3D%203.14%5Ctimes%20361)
∴ Area of circle A= 1133.54
Circumference of circle= 2πr
Circumference of Circle A= ![2\times 3.14\times 19= 119.32](https://tex.z-dn.net/?f=2%5Ctimes%203.14%5Ctimes%2019%3D%20119.32)
∴ Circumference of Circle A= 119.32