SOLUTION: A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What      Log On

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Question 104677: A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What must be the width of the walkway to the nearest thousandth?
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Area=length*width
____=30ft*40ft
____=1200 sq. ft
Let x= the width of the walkway
Then, the new length of the whole space is 40+2x and the new width is 30+2x
The total area, garden plus walkway, is to be 1800 sq. ft. So,
__________________________%2840%2B2x%29%2A%2830%2B2x%29=1800____________________________
____________________40%2A%2830%2B2x%29%2B2x%2A%2830%2B2x%29=1800____________________________
____________________%281200%2B80x%29%2B%2860x%2B4x%5E2%29=1800____________________________
______________________1200%2B%2880x%2B60x%29%2B4x%5E2=1800____________________________
______________________1200%2B140x%2B4x%5E2-1800=1800-1800_______________________
__________________________-600%2B140x%2B4x%5E2=0________________________________
___________________________4x%5E2%2B140x-600=0________________________________
_______________________%281%2F4%29%2A%284x%5E2%2B140x-600%29=%281%2F4%29%2A0______________________
_____________________________x%5E2%2B35x-150=0________________________________
By the quadratic formula,
x=%28-35%2B-sqrt%2835%5E2-4%2A1%2A%28-150%29%29%29%2F%282%2A1%29
x=%28-35%2B-sqrt%281225%2B600%29%29%2F%282%29
x=%28-35%2B-sqrt%281825%29%29%2F%282%29
x=%28-35%2B42.72%29%2F%282%29 or x=%28-35-42.72%29%2F%282%29
x=3.85 or x=-38.6
The negative result will not be ACCEPTED for there's no such things such as NEGATIVE LENGTH!

Therefore, the length must be 3.85 ft wide!

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HyperBrain!