Answer:
Radius of larger flower bed = 10 feet
Radius of smaller flower bed = 6 feet
Step-by-step explanation:
<u>Complete question:</u>
"You have two circular flower beds, as shown. The sum of the areas of two flower beds is 136 pi square feet. Find the radius of each bed.<em>"</em>
<em>Radius of larger flower bed = r</em>
<em>Radius of smaller flower bed = r - 4</em>
<em />
Now,
Area of circle is ![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
Since, total area is
, we can write:
![\pi r^2 + \pi (r-4)^2=136\pi](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%20%2B%20%5Cpi%20%28r-4%29%5E2%3D136%5Cpi)
Expanding and solving for r:
![\pi r^2 + \pi (r-4)^2=136\pi\\r^2+(r-4)^2=136\\r^2 + r^2 - 8r + 16 = 136\\2r^2-8r-120=0\\2(r+6)(r-10)=0\\r=-6,10](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%20%2B%20%5Cpi%20%28r-4%29%5E2%3D136%5Cpi%5C%5Cr%5E2%2B%28r-4%29%5E2%3D136%5C%5Cr%5E2%20%2B%20r%5E2%20-%208r%20%2B%2016%20%3D%20136%5C%5C2r%5E2-8r-120%3D0%5C%5C2%28r%2B6%29%28r-10%29%3D0%5C%5Cr%3D-6%2C10)
Radius cannot be negative, so r = 10 & r-4 = 10 -4 = 6
Radius of larger flower bed = 10 feet
Radius of smaller flower bed = 6 feet