Q:

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.

Accepted Solution

A:
Answer:Radius of larger flower bed = 10 feetRadius of smaller flower bed = 6 feetStep-by-step explanation:Complete question:"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."Radius of larger flower bed = rRadius of smaller flower bed = r - 4Now,Area of circle is  [tex]\pi r^2[/tex]Since, total area is [tex]136\pi[/tex], we can write:[tex]\pi r^2 + \pi (r-4)^2=136\pi[/tex]Expanding and solving for r:[tex]\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[/tex]Radius cannot be negative, so r = 10  &  r-4 = 10 -4 = 6Radius of larger flower bed = 10 feetRadius of smaller flower bed = 6 feet