Question 178628
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Area formula:  *[tex \Large A = lw].  Since *[tex \Large l = x], *[tex \Large w = x - 9], and A is given as 220, just substitute.



*[tex \Large x(x -9) = 220]. 


Distribute and add -220 to both sides:


 
*[tex \Large x^2 - 9x - 220 = 0].


Since *[tex \Large -20 \times 11 = -220] and *[tex \Large -20 + 11 = -9], this quadratic factors.


The quadratic, of course, has two roots.  One of these roots will be negative which is an absurd result when calculating the length of something.  This is an extraneous root introduced when the variable was squared in the process of solving the problem -- exclude it.  The positive root is the correct value for the length of the rectangle, and the width can be calculated directly from that value.


You should be able to handle it from here. 


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