SOLUTION: A circular garden is surrounded by a sidewalk with a uniform width of 14 feet. The total area of the sidewalk equals the total area of the garden. How many feet are in the diameter

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Question 269738: A circular garden is surrounded by a sidewalk with a uniform width of 14 feet. The total area of the sidewalk equals the total area of the garden. How many feet are in the diameter of the garden? Round your answer to the nearest whole number.
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A circular garden is surrounded by a sidewalk with a uniform width of 14 feet. The total area of the sidewalk equals the total area of the garden. How many feet are in the diameter of the garden? Round your answer to the nearest whole number.
:
Let r = radius of the garden
then
(r+14) = radius of the garden and walkway
:
From the given information we know the overall area = twice the garde area
:
= 2()
divide both sides by pi
= ()
FOIL
= ()
= 0
= 0
= 0; multiplied by -1
Use the quadratic formula to find r: a=1; b=-28; c=-196
Positive solution: r = 33.8
then
33.8 * 2 = 67.6 ~ 68 ft is the diameter of the garden

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = the radius of the circular garden

The radius of the garden + sidewalk is

And, the problerm says , so

use quadratic formula

The diameter of the garden is 67 ft
check:

close enough