SOLUTION: The length of a rectangle is 10 m less than twice the width of the rectangle. The area is 2800 m2. Find the length and width of the rectangle. I know that the length =2w-10 an

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Question 3289: The length of a rectangle is 10 m less than twice the width of the rectangle. The area is 2800 m2. Find the length and width of the rectangle.
I know that the length =2w-10 and thatLxW=2800 so 2800=W (2W-10) is that right ? and where do i go from there I know there is an answer i figured it out its W=40 lenght is 70 (because it= 2800) how to I write down the formula and how di solve the formula help
Answer by drglass(89) About Me  (Show Source):
You can put this solution on YOUR website!
You are certainly correct so far. You have W%282W-10%29+=+2800. To finish this, complete the multiplication on the right-hand side 2W%5E2+-+10W+=+2800. Now subtract 2800 from both sides to get 2W%5E2+-+10W+-+2800+=+0. We can factor this a little further to get 2%28W%5E2+-+5W+-+1400%29+=+0. Now, you either have to be very observant or you have to know the quadratic formula. The quadratic formula tells us that the solution to this equation is:

%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29

The values for a, b and c are 1, -5 and -1400 respectively. This gives solutions at:

%285+%2B-+sqrt%2825%2B5600%29%29%2F2

The square root of 5625 is 75, so the solutions for this equation are 40 and -35. Well, you can't have a width of -35, so the width must be 40 and the length must be 70.