SOLUTION: Good day! kindly help me with this word problem. Thanks! A park department gardener wants to plant a border of flowers along the edges of an 8 feet by 6 feet rectangular bed. H

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Question 640415: Good day! kindly help me with this word problem. Thanks!
A park department gardener wants to plant a border of flowers along the edges of an 8 feet by 6 feet rectangular bed. How wide should he make the border if he wants the remaining unplanted area to be one-half the area of the entire flower bed?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A park department gardener wants to plant a border of flowers along the edges
of an 8 feet by 6 feet rectangular bed
How wide should he make the border if he wants the remaining unplanted area
to be one-half the area of the entire flower bed?
:
Find the area of the flower bed; 8 * 6 = 48 sq ft
Then half that area = 24 sq/ft
Then the total area: 24 + 48 = 72 sq/ft
:
Let w = width of the border
The overall dimensions including the border:
(2w+8) by (2w+6)
:
Overall area
(2w+8)*(2w+6) = 72
FOIL
4w^2 + 12w + 16w + 48 = 72
4w^2 + 28w + 48 - 72 = 0
A quadratic equation
4w^2 + 28w - 24 = 0
Simplify, divide by 4
w^2 + 7w - 6 = 0
Use the quadratic formula to find w, a=1; b=7; c= -6
w+=+%28-7+%2B-+sqrt%287%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29+
do the math here, should get a positive solution of
w = .772 ft is the width of the border