SOLUTION: Joe's rectangular garden is 6 meters long and 4 meters wide. He wishes to double the area of his garden by increasing its length and width by the same amount. Find the number of me
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Question 990874: Joe's rectangular garden is 6 meters long and 4 meters wide. He wishes to double the area of his garden by increasing its length and width by the same amount. Find the number of meters by which each dimension must be increased. Answer by macston(5194) (Show Source):
You can put this solution on YOUR website! .
L=length; W=width; X=amount of increase; A=area
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(L+X)(W+X)=2(LW)
(6m+X)(4m+X)=2(6m)(4m)
X^2+10X+24=48
X^2+10X-24=0
(X-2)(X+12)=0
(X-2=0) OR (X+12=0)
X=2 OR X=-12 Since -12 makes no sense,
X=2 meters
ANSWER: Increase each dimension by 2 meters.
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CHECK
(L+X)(W+X)=2(LW)
(6m+2m)(4m+2m)=2(6m)(4m)
(8m)(6m)=2(24m^2)
48m^2=48m^2
