Two circles have circumferences that add up to 12π centimeters. the sum of their areas is 20π. what is the radius of each circle?

Let x = the radius of the first circle

Let y = the radius of the second circle

Since the perimeter (better known as circumference) of a circle is 2pi * r and area is pi*r^2 we get the following equations:

2pi * x + 2pi * y = 12pi

Pi * x^2 + pi * y^2 = 20pi

Since the second equation is not linear, we will use the substitution method.

2pi * y = 12pi - 2pi*x

Then divide both sides 2pi

Y = 6 - x

Now we’ll substitute this into the other equation:

Pi * x^2 + pi * (6 - x) ^2 = 20pi

Simplifying. Get rid of the pi’s by dividing both sides by it:

x^2 + (6 - x) ^2 = 20

since the equation is quadratic, simply and get one side to equal to 0.

X^2 + 36 - 12x + x^2 = 20

2x^2 - 12x + 36 = 20

2x^2 - 12x + 16 = 0

Now we solve this by factoring.

2 (x^2 - 6x + 8) = 0

2 (x - 4) * (x-2) = 0

By using the zero property ... we can get ...

X - 4 = 0 or x - 2 = 0

Which gives us x = 4 and x = 2

Since x is the radius of one circle, we need to compute for y, and the other circle’s radii. We can get y using our x values and the equation y = 6 - x.

For x = 4:

y = 6 - 4 = 2

For x = 2

y = 6 - 2 = 4

The radii are 2 and 4.