Question 1041078: A rectangle with an area of 500 feet has a length that is 30 feet longer than twice its width. How many feet is the length of the rectangle?
Having trouble figuring out these rectangle word problems, I'm terrible at coming up with the actual equation, any help is much appreciated.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! A=L*W
L=2W+30, that is 30 more than 2W.
A=(2W+30)*W=500 sq ft
Now multiply this out
2W^2+30W=500. Notice that this looks like a quadratic, except it doesn't equal 0.
subtract 500 on both sides
2W^2+30W-500=0 Now it does.
divide by 2. You don't have to, but it makes it easier
2(W^2+15W-250)=0
since 2 can't equal 0,
W^2+15W-250=0 (same as dividing by 2 both sides)
facto, noting that 25 and 15 can make 10 if one is subtracted from the other.
(W+25)(W-10)=0, set each of them equal to 0
W=-25 feet, which makes no sense.
W=10 feet
The width is 10 feet
the length is 2W+30=50 feet ANSWER. Be sure that instead of W, you answer the question, which is the length.
The area is 500 sq ft
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