SOLUTION: Two circles have perimeters that add up to 12π centimeters and areas that add up to 20π square centimeters. Find the radius of each circle. Give exact answers.

Question 229541: Two circles have perimeters that add up to 12π centimeters and areas that add up to 20π square centimeters. Find the radius of each circle. Give exact answers.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Let x = the radius of the first circle
Let y = the radius of the second circle circle

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

Since the second equation is not linear, we'll use the Substitution Method to solve this system. We'll solve the first equation for y. Start by subtracting from each side:

Divide both sides by :

Now we'll substitute this into the other equation:

Simplifying. We'll get rid of the 's by dividing both sides by it:

Since this is a quadratic equation we'll simplify and get one side equal to zero:

Now we solve this by factoring or by using the quadratic equation. This will factor fairly easily:

By the Zero Product Property we know that this product can be zero only if one of the factors is zero. The factor of 2 cannot be zero but the other two factors can:
or
which gives us:
or

Remember to answer the question. (With word problems it is always tempting to feel satisfaction with having solved for the variable and forget to answer the question.

The question here is to find the two radii. Since x is the radius of one circle, we need to find y, the radius of the other circle, too. 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

So even though we came up with 2 x values, there is only one solution. The radii are 2 and 4.
RELATED QUESTIONS
two circles have circumferences that add up to 12(pie) centimeters, and areas that add up (answered by lwsshak3)

What two factors of -375 that add up to... (answered by Edwin McCravy)

sided figure that add up to 10 boxes and they add up to 20. you can only use 1-12 one... (answered by stanbon)

find 3 next door numbers that add up to... (answered by Fombitz)

if you have some coins that add up to $1.48, then how can I find the least number of... (answered by CubeyThePenguin)

What are two numbers that multiply to be -60 and add up to... (answered by Alan3354)

A square has a perimeter of 36 centimeters. A smaller square has a side length of 4... (answered by TimothyLamb)

The areas of two similar rectangles add up to 39 square units. Twice the area of... (answered by Theo)

Kim need to add a 6% saline solution to an iv bag that contains 20 cubic centimeters of a (answered by josgarithmetic)

SOLUTION: Two circles have perimeters that add up to 12&#960; centimeters and areas that add up to 20&#960; square centimeters. Find the radius of each circle. Give exact answers.

SOLUTION: Two circles have perimeters that add up to 12π centimeters and areas that add up to 20π square centimeters. Find the radius of each circle. Give exact answers.