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.