Question

The area in square feet of a rectangle field is X squared -100 X +2100. The width, and feet, is X -30. What is the length in feet

Answer 1

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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