SOLUTION: The plowed are of a field is a rectangle 80 feet by 120 feet. The owner plans to plow an extra strip of uniform width on each four sides of the field, in order to double the plowed

Question 71109: The plowed are of a field is a rectangle 80 feet by 120 feet. The owner plans to plow an extra strip of uniform width on each four sides of the field, in order to double the plowed area. How many feet should he ass to each dimension?
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
80*120=9600 SQ FT IS HIS ORIGINAL AREA
THUS 2*9600=19200 WHEN HE DOUBLES IT
THUS (80+2X)(120+2X=19200
9600+240X+160X+4X^2=19200
4X^2+400X+9600-19200=0
4X^2+400X-9600=0
X^2+100X-2400=0
(X-20)(X+120)=0
X-20=0
X=20 ANSWER FOR THE INCREASE WIDTH ON ALL FOUR SIDES TO DOUBLE HIS AREA.
PROOF
(80+2*20)(120+2*20)=19200
(80+40)(120+40)=19200
120*160=19200
19200=19200
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