SOLUTION: A garden area is 30 ft. long and 20 ft. wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A garden area is 30 ft. long and 20 ft. wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path.       Log On


   

Question 82339: A garden area is 30 ft. long and 20 ft. wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path.
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
30*20=600 THE ORIGINAL AREA
(30-2X)(20-2X)=400 THE REMAINING GARDEN
600-40X-60X+4X^2=400
4X^2-100X+200=0
X^2-25X+50=0
USING THE QUADRATIC EQUATION WE GET:
X=(25+-SQRT[-25*-25-4*1*50])/2*1
X=(25+-SQRT[625-200])/2
X=(25+-SQRT425)/2
X=(25+-20.6)/2
X=(25+20.6)/2
X=45.6/2
X=22.8 NON ANSWER.
X=(25-20.6)/2
X=4.4/2
X=2.2 ANSWER FOR THE WIDTH OF THE PATH.
PROOF
(30-4.4)*(20-4.4)=400
25.6*15.6=400
400=400