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Question 66294: i need help answering this equation with factoring:
"the length of a rectangle is 6 meters more than twice the width. if the area of the rectangle is 140 meters^2,find the dimensions."
i tried but i couldnt get it.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! i need help answering this equation with factoring:
"the length of a rectangle is 6 meters more than twice the width. if the area of the rectangle is 140 meters^2,find the dimensions."
i tried but i couldnt get it.
Let w=width
Then length, l=2w+6
Now we know that the Area, A=l times w
So our equation to solve is:
w(2w+6)=140; w(2w+6)=2w^2+6w a(b+c)=ab+ac (distributive law)
2w^2+6w=140 subtract 140 from both sides:
2w^2+6w-140=0 Divide through by 2
w^2+3w-70=0 This is in the standard form for a quadratic equation where:
a=1
b=3
c=-70
If the quadratic is factorable and a=1, then b is the sum of the factors of c.
What are the two factors of -70 that adds up to +3??
Is it -70 and +1?----------------no
Is it -35 and +2?---------------no
Is it +10 and -7-------------yes!!!!!!!!!! this works
So: w^2+3w-70=0
(w+10)(w-7)=0
w=-10 meters; widths cannot be negative so w=7 is the correct answer
w=7 meters
l=2w+6=2(7)+6
l=20 meters
ck
area=(l)(w)
140=(7)(20)
140=140
l=2w+6
20=(2)(7)+6
20=20
Hope this helps-----ptaylor
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