SOLUTION: This is a word problem that I'm sure uses the quadratic formula because this is what the chapter is about! The formula seems simple enough, but I don't know how to set this up.

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Question 49033This question is from textbook Beginning Algebra
: This is a word problem that I'm sure uses the quadratic formula because this is what the chapter is about! The formula seems simple enough, but I don't know how to set this up.
A garden area is 30ft. long and 20ft. wide. A path of uniform width is set around the edge. If the remaining garden are is 400ft^2, what is the width of the path?This question is from textbook Beginning Algebra

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
This is a word problem that I'm sure uses the quadratic formula because this is what the chapter is about! The formula seems simple enough, but I don't know how to set this up.
A garden area is 30ft. long (L)and 20ft. wide(W). A path of uniform width is set around the edge. If the remaining garden are is 400ft^2, what is the width of the path?
LET THE WIDTH OF PATH =X
L=30'............W=20'
LENGTH OF INNER RECTANGLE=L'=L-2X=30-2X
WIDTH OF INNER RECTANGLE=W'=W-2X=20-2X
HENCE REMAINING GARDEN AREA=L'*W'=(30-2X)(20-2X)=400
600-60X-40X+4X^2=400
4X^2-100X+200=0
X^2-25X+50=0
X=[25-SQRT(25^2-4*50)]/2=2.19'