SOLUTION: Please Explain: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please Explain: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of       Log On


   

Question 49045: Please Explain:
A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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Question 49045: Please Explain:
A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be?: Please Explain:
LET THE WIDTH OF PATH =X
L=32'............W=24'
LENGTH OF INNER RECTANGLE=L'=L-2X=32-2X...SINCE ON BOTH SIDES PATH TAKES X+X FEET LEAVING 32-2X FOR THE GARDEN PROPER.
WIDTH OF INNER RECTANGLE=W'=W-2X=24-2X
HENCE REMAINING GARDEN AREA=L'*W'=(32-2X)(24-2X)=425
768-64X-48X+4X^2=425
4X^2-112X+343=0..THIS IS A QUADRATIC.OF TYPE AX^2+BX+C=0
ITS ROOTS ARE
X=[-B+ OR - SQRT.{B^2-4AC}]/2A
WE HAVE HERE A=4..B=-112...C=343...SO
X=[112-SQRT(112^2-4*4*343)]/8= 3 '


SEE THE FOLLOWING EXAMPLE AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK
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'