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vodka [1.7K]
3 years ago
11

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 e

ach bed.
Mathematics
1 answer:
finlep [7]3 years ago
8 0

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

Since, total area is 136\pi, we can write:

\pi r^2 + \pi (r-4)^2=136\pi

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

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

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