Question 1086553
<font color="black" face="times" size="3">L = length (in inches)
W = width (in inches)


We're given that the "the length...is 9 inches more than its width", so


{{{L = W+9}}}


The area of any rectangle is found by the formula 


{{{A = L*W}}}


Make substitutions and get everything to one side


{{{A = (W+9)*W}}} Replaced L with W+9


{{{112 = (W+9)*W}}} Replaced A with 112


{{{112 = W*W + 9*W}}}


{{{112 = W^2 + 9W}}}


{{{112-112 = W^2 + 9W - 112}}}


{{{0 = W^2 + 9W - 112}}}


{{{W^2 + 9W - 112 = 0}}}


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From here use the quadratic formula. It is the most effecient way to solve quadratic equations. 


Using the quadratic formula, we get


{{{W = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{W = (-(9)+-sqrt((9)^2-4(1)(-112)))/(2(1))}}} Plug in {{{a = 1}}}, {{{b = 9}}}, {{{c = -112}}}  


{{{W = (-9+-sqrt(81-(-448)))/(2)}}}


{{{W = (-9+-sqrt(81+448))/(2)}}}


{{{W = (-9+-sqrt(529))/2}}}


{{{W = (-9+sqrt(529))/2}}} or {{{W = (-9-sqrt(529))/2}}}


{{{W = (-9+23)/2}}} or {{{W = (-9-23)/2}}}


{{{W = 14/2}}} or {{{W = -32/2}}}


{{{W = 7}}}    or    {{{W = -16}}}


Ignore the value {{{W = -16}}}. It's not possible to have a negative width.


The only practical solution is {{{W = 7}}} 


If the width is {{{W = 7}}}, then the length L is


{{{L = W+9}}}


{{{L = 7+9}}}


{{{L = 16}}}


Note how L*W = 7*16 = 112 so that helps confirm the answers.


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Answers: 
<font color=red>Length = 16 inches
Width = 7 inches</font>
</font>