Answer: The length is: "(x − 70)" ft.
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Area (A) = Length (L) * width (w) ; that is:
A = L * w ;
We want to solve for the "Length" (L)" ;
So, we can rearrange the equation:
A / w = (L* w) / w ;
to get: A / w = L ;
↔ L = A / w ;
A = (x² − 100x + 2100) ;
w = (x − 30)
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L = (x² − 100x + 2100) / (x − 30) ;
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So; (x − 30) * _?__ = x² − 100x + 2100 ?? ,
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-30 * _?_ = 2100 ? ; → 2100 ÷ (-30) = -70 ;
-30 − 70 = ? -100?? Yes!
So, the answer is: "(x − 70)" ;
That is: " (x − 30) (x − 70) = x² − 100x + 2100 .
The Length is: "(x − 70)" ft.
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