SOLUTION: A rectangular parking lot has a width that is eight feet less than its length. Surrounding the parking lot is a sidewalk measuring three feet wide. What are the dimensions of the p

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Question 978796: A rectangular parking lot has a width that is eight feet less than its length. Surrounding the parking lot is a sidewalk measuring three feet wide. What are the dimensions of the parking lot if the total area of the parking lot and sidewalk is 2288ft^2?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular parking lot has a width that is eight feet less than its length.
Surrounding the parking lot is a sidewalk measuring three feet wide.
What are the dimensions of the parking lot if the total area of the parking lot and sidewalk is 2288ft^2?
:
let x = width of the parking lot
then
(x+8) = the length
:
The 3' sidewalk adds 6 ft to the length and the width of the parking lot
An area equation, overall length times overall width
(x+8+6)*(x+6) = 2288
(x+14)*(x+6) = 2288
FOIL
x^2 + 6x + 14x + 84 = 2288
Combine to form a quadratic equation
x^2 + 20x + 84 - 2288 = 0
x^2 + 20x - 2204 = 0
You can use the quadratic formula but this will factor to:
(x+58)(x-38) = 0
the positive solution is all we want here
x = 38 ft is the width of the parking lot
and
38 + 8 = 46 ft is the length
:
:
Check this by adding 6' to the length and the width and finding the area
44 * 52 = 2288