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
RELATED QUESTIONS
A homeowner plants two flower beds around his garage. What is the total area he will have (answered by JulietG)

The adjoining figure shows the location of four flower beds in a park. If the outer... (answered by josgarithmetic)

A math assessment question: Ericka planted 4 flower beds in her garden. She spread... (answered by ikleyn)

Below was a school assessment question: "Ericka planted 4 flower beds in her garden.... (answered by ikleyn)

roberta works in her garden every day. she spends 70% of that time weeding her flower... (answered by longjonsilver)

The length of a rectangular flower bed is 40cm and breadth is 10cm.The length of a square (answered by mananth)

Hi I'm sorry I'm not sure if this went through as I accidentally hit send before I was (answered by ankor@dixie-net.com)

Chris wants to make a pair of raised beds for her garden. She wants the beds to share a... (answered by richwmiller)

Pine bark mulch 0.5ft deep is spread in each of the flower beds shown. Mulch is sold by... (answered by checkley79)