SOLUTION: The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width
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-> SOLUTION: The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width
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Question 1049197: The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width with the same area as the flower bed. Calculate the perimeter of the outside of the path.
a) set up a quadratic equation to model the situation
b) use the quadratic formula to solve the problem Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The parks department is planning a new flower bed outside city hall.
It will be rectangular with dimensions 9m by 6m.
The flower bed will be surrounded by a path of constant width with the same area as the flower bed.
Calculate the perimeter of the outside of the path.
:
the area of the flower bed: 9*6 = 54 sq/m, (also the area of the path)
:
a) set up a quadratic equation to model the situation
let w = the width of the path around the flower bed
then
(2w+9) by 2w+6) = the overall dimensions (garden and path)
:
the overall area - flower bed area = path area
(2w+9)*(2w+6) - 54 = 54
FOIL
4w^2 + 12w + 18w + 54 - 54 - 54 = 0
A quadratic equation
4w^2 + 30w - 54 = 0
simplify, divide by 2
2w^2 + 15w - 27 = 0
:
b) use the quadratic formula to solve the problem
2w^2 + 15w - 27 = 0; factors to:
(2w-3)(w+9) = 0
The positive solution is all we want here
2w = 3
w = 1.5 m is the width of the path
:
"Calculate the perimeter of the outside of the path."
Find the overall dimensions
2(1.5) + 9 = 12m long
2(1.5) + 6 = 9m wide
P = 2(12) + 2(9)
p = 42 meters is the perimeter
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