SOLUTION: two circular flower beds have a combined area of 29/2pie metre. the sum of the circumferences of the two flower beds is 10pie metre. determine the radius of each flower bed.
Question 473001: two circular flower beds have a combined area of 29/2pie metre. the sum of the circumferences of the two flower beds is 10pie metre. determine the radius of each flower bed. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! two circular flower beds have a combined area of 29/2pie metre. the sum of the circumferences of the two flower beds is 10pie metre. determine the radius of each flower bed.
:
Let a = radius of the 1st circular flower bed
Let b = radius of the 2nd one
:
Combined areas + = ()
divide thru by pi + =
we can also write it:
a^2 + b^2 = 14.5
:
Combined Circumferences + =
divide thru by 2pi
a + b = 5
b = (5-a)
:
In the 1st equation replace b with (5-a)
a^2 + (5-a)^2 = 14.5
a^2 + 25 - 10a + a^2 = 14.5
2a^2 - 10a + 25 - 14.5 = 0
2a^2 - 10a + 10.5 = 0
Simplify, divide by 2
a^2 - 5a + 5.25 = 0
This factors to:
(a-1.5)(a-3.5) = 0
Two solutions
a = 1.5, then b = 3.5
a = 3.5, then b = 1.5
