SOLUTION: Julia's soybean field is 3 m longer than it is wide. To increase her production, she plans to increase both the length and width by 2 m. If the new field is 46m2 larger than the

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Question 123075: Julia's soybean field is 3 m longer than it is wide. To increase her production, she plans to increase both the length and width by 2 m. If the new field is 46m2 larger than the old field then what are the dimensions of the the old field?
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X & X+3 ARE THE MEASUREMENTS OF THE ORIGINAL FIELD.
X(X+3)=X^2+3X FOR THE ORIGINAL FIELDS AREA.
(X+2)(X+5)=X^2+7X+10 IS THE EXPANDED AREA.
GIVEN THAT THE DIFFERENCE IS 46M^2 THEN WE HAVE:
X^2+3X+46=X^2+7X+10
X^2-X^2+3X-7X=-46+10
-4X=-36
X=-36/-4
X=9M FOR ONE OF THE ORIGINAL WIDTH.
9+3=12M FOR THE ORIGINAL LENGTH.
9*12=108 M^2 FOR THE ORIGINAL FIELD.
PROOF:
9+2=11 & 12+2=14
11*14=154 M^2
154-46=108
108=108