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Assign the rectangle a width 'x'. From the data in the problem the height is then '2x+1'. Multiplying the two together gives the area of the rectangle, which we know to be 45. In equation for this is: x(2x+1) = 45 or 2x^2 + x = 45. The roots of this equation can then be found either through the quadratic equation or a calculator solver (I used the solver because I'm lazy) and the answers are x = -5 and x= 4.5. The rectangle has a width of 4.5 and a height of 10.

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Q: The length of a rectangle is 1 more than twice its width and the area of the rectangle is 45 what are the dimensions of the rectangle?
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