Answer:
Step-by-step explanation:
You want the length and width of a rectangle that is 10 ft longer than wide if adding 10 ft to each dimension doubles its area.
The original area will be the product of the length and width:
A = LW = (W+10)W
The area with increased dimensions is ...
A = (L+10)(W+10)
We want the increased area to be twice the original area:
2(W+10)(W) = ((W+10)+10)(W+10) . . . . . . use W+10 for L
2W = W +20 . . . . . . . . divide both sides by W+10
W = 20 . . . . . . . . . . subtract W
The original width is 20 ft. The original length is 30 ft.
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Additional comment
If we were to write the equation for area in standard form, it would be a quadratic in W. One of its factors would be (W+10). We can divide that out because we know that W=-10 is not a solution.